 Hello everyone. Sorry for the disembodied voice routine, but these sorts of problems, I think, require you to pay much more attention to what's written on the screen than my facial expressions. So what we're going to do here this time around is we're going to actually symbolize propositions. We've gone through truth relations, we've gone through terms and definitions, and now we're going to have to actually start assigning variables to sentences. This will result in kind of a calculus for these arguments. So the first thing, the first rule for these symbolizations are the variables, the letters that we're going to use to represent atomic propositions. I'm going to use these for atomic propositions. So the first rule is to use P, Q, R, and so on through Z for atomic propositions. Do this in order, right? Don't start with A, B, C, or D, and don't start with T, start with P. So this is the first rule, P, Q, R, and so on for these atomic propositions. One of the reasons why I'm being so personic about this is that you will be completing a homework on canvas, and there needs to be a uniform way for you to complete these return in these assignments. So it's one of the reasons why we have such strict rules. So what's this look like? Well, take a look at this sentence here, right? So we're trying to, again, follow this rule. Morality is justified by cultural belief. Only if our culture is morally impeccable. So just look at that first sentence. So the first thing you need to do is to identify the atomic propositions. And morality is justified by cultural belief. That's the first atomic proposition. That's the first atomic proposition. And the phrase here, only if is our logical connective. And only if, if you remember, gives us a conditional. And the only if, what follows the only if indicates the consequent what occurs before the only is the antecedent. And this gives us, this leads us to our second atomic proposition. Our culture is morally impeccable. Okay, so this is the first sentence. Morality is justified by cultural belief. Only if our culture is morally impeccable. So this gives us two atomic propositions and our logical connected. So this already tells us that we got a conditional. Okay, so let's just concentrate then upon this first rule and assigning a letter to the first atomic proposition. Well, following a rule one, the first atomic proposition, morality is justified by cultural belief. That will be assigned P. Okay. That's assigned P. So that's our first atomic proposition. What about our second? Again, following rule one, we got our second proposition here. Our culture is morally impeccable. That will be assigned Q. Right. So again, in order. So you so the first atomic proposition you get, that's assigned P. The second atomic proposition you get, that's assigned Q. That's our rule one. First proposition is assigned P. Second proposition assigned Q. Don't start with D. Don't start with T. Now you start with P and go on from there. And don't skip, right? Don't go P, T. So P, Q, R, S, T, U, V, W, so on. Okay. So we've got our truth assignment. We got our variables. Excuse me. We got our variables for our first two atomic propositions. Well, let's take a look in the next sentence. And the next sentence starts off with either. So that already tells us the disjunction. And more than that, we got either it is false set. So we got this should tell us right away, we've got a disjunction of negations. Let's take a look at the atomic proposition part. Our culture is morally impeccable. Well, this should look really familiar. After all, that's our assignment for Q. Now you might say, well, then I'll assign this R. No, this brings us to our second rule. Use the same letter for the same atomic proposition throughout the argument. That's the second rule. Use the same letter for the same atomic proposition throughout the argument. So our culture is morally impeccable. That gets assigned Q still, right, still. Okay, so I had here it's it's false that, right? Yeah, that tells us we got a disjunction. That's how we got a negation here. All right, even though this is a negation, right, the atomic proposition part still is assigned Q. This isn't a new time proposition is still the same atomic proposition. Also notice that we got, you know, either or happening here. Okay. That's so that that's another logical connective. And we got the second it is false that. All right. One of this brings us to, you know, it's always brings us to our third atomic proposition and the argument. And that's something needs to change in our culture. All right. So following rule one rule two, it's assigned R. And since it's a new proposition, that's why it gets R, right? Okay, so let's take a look at the next one. See if we have any more new atomic propositions. Well, the next one is something needs to change in our culture. Well, we just dealt with that. So it's so following rule two, it still has arm as its letter. And the last atomic problem we got. Yeah, however, however, it's just a connecting word. It's actually not even a logical connective. This is just more to indicate sort of mood sort of sort of thing. But sometimes that helps to use these sorts of connecting words in order to indicate the flow of the argument and that you're still providing premises, for instance. Okay, so the next thing we have is it is false that that's the logical connective. The word so there, I haven't highlighted it, but the word so that indicates the conclusion. If you remember from that, those sets of those sets of assignments are back there, that indicates the conclusion. And the atomic proposition part of it is morality is just by the cultural belief. Well, that was our first, a first atomic proposition. So it's still assigned P. So rule one and rule two, use P Q and R to for the atomic propositions, start at P, work in succession all the way up to Z, sign a letter for the atomic propositions. And if an atomic proposition gets a letter, use the same letter for all of it. Okay, so that's atomic propositions. Let's start taking a look at some of the complex propositions, complex propositions. So we will symbolize negations. All right, remember negation is a logical connective, although just, it's just assigned to the one letter. We'll use the minus sign for negations. And if on a standard QWERTY keyboard, that's Q, W, E, R, T, Y. If you never heard of this, right, this is the standard sort of keyboard where the letters are set up. And the you're looking at upper, you know, the second row, starting a Q, Q, W, E, R, T, Y. That's quite, that's why it's called a QWERTY keyboard. Little bit of nerd trivia there for you. On a standard QWERTY keyboard, we'll use the minus sign for negation. So that will go immediately before the proposition to indicate a negation. I want to be careful. Do not use shift minus, right? That produces a dash. That's a different symbol. The computer recognizes these two different symbols, right? Do not use a dash, right? Do not use a dash. So it's not shift and and then the minus button. Just the minus button. Okay. Just the minus button. All right. So we're going to assign a letter for each negation. Sign a letter for each negation. We're going to stick with this same argument, right? We'll stick with the same example that we're dealing with. So looking at this first negation here, it's in the second sentence. It is false that our culture is more than impeccable. And we got a second negation. It is false that something needs to change in our culture. Now, let's just go with the first one, right? It is false that our culture is more than impeccable. Well, we already signed a letter assignment to this, right? Where we saw that. So following rule one and rule two, and now our symbol for negation, this is given, you know, not Q, right? That minus Q, not the dash Q minus Q. And the second negation, you know, something needs to change in our culture, or it's false that something needs to change in our culture. Well, it had a assignment too for a letter, and that was R. So this is symbolized as minus R, minus R. And that's how we symbolize negations within the physiological formula. Let's take a look at conjunctions. To symbolize a conjunction, we're going to use the ampersand. That's what this thing is called, right? If you look at that little symbol above the seven, it's called an ampersand. So you produce that with a shift seven to produce that ampersand, or you might have just called it the and symbol. So that's what we use for conjunctions. Now, I have to change examples here to illustrate a conjunction. So there are fish in these waters, and this is good bait. So if we're going to sign, we're going to turn this into a logical formula. Well, first we have to identify the two atomic propositions. There are fish in these waters. That's the first one. And this is good bait. That's the second one. And we have the logical connected between and. So following rule one, there are fish in these waters, that gets P. Falling rule one and rule two, this is good bait. That gets Q. So if we're going to symbolize this conjunction, there are fish in these waters, and this is good bait. We use that with P, ampersand, Q. So I want to point out here, when we dealt with negations, there should be no space between the minus symbol and the proposition. No space for negations between the minus symbol and the propositions. For pretty much everything else, when we deal with conjunctions, there should be a space between the proposition and the ampersand and the falling proposition. And there should be one and only one space showing this. You have to be precise when you type this into the computer. Otherwise the computer is not going to count it wrong. It's not going to recognize that sort of simple error. So if we're doing a conjunction, we got the proposition, ampersand, and the second proposition, and that should be separated by space each. All right, let's take a look at disjunctions. Disjunctions, if you remember, give us subcontrariety. Or if we've got a disjunction of negations, that's contrariety. But to symbolize a disjunction, we're going to use just the lowercase v, not an uppercase, just the lowercase v. So just press the v button. So let's see what this looks like with our example that we dealt with. The either or indicates a disjunction. That tells us we've got a disjunction. And we also have to pay note to the negations, that those are in there too, the negations. So we had to account for those two in our symbolization. And these are our two atomic propositions. Now, so we've got to keep in mind, we already covered how to symbolize negations, so we're going to use this here in our symbolization, but we also got the disjunction. Now remember following, so our proposition here is either it's false that our culture is morally critical, or it's false that something needs to change in our culture. Well, remember following rule one and rule two, that first atomic proposition got q, that second atomic proposition got r. And we looked at how to symbolize the negation, so it would be minus q and minus r for the two negations. But then to symbolize the disjunction of those two, we have that little lowercase v in the middle. And again, there's a space between the first proposition and the logical connective and the single space between the logical connective and the second proposition when dealing with the disjunctions. The minus symbol, not similar to that, minus symbol needs to be right up next to the proposition. But the disjunction and conjunction, there's a space separating the logical connector from the two propositions, from the two disjuncts in this case. All right, let's take a look at conditionals. Conditionals are a little different. We're going to use the graded end symbol, so that's right over here. Or you might think it was a right arrow symbol, if you really want to think of it that way. And you use it by pressing that shift button and that button there for the right arrow on the quarter keyboard. And that's going to give us the antecedent will be on the left hand side of the symbol, and the consequent will be on the right hand side of the symbol. Okay, so we've got our example here, and it has it happens. We've got a logical connected that indicates a conditional. Remember that? And we have the two atomic propositions. And following rule one and rule two, if you remember before that first one got a P and the second one got a Q. So that's our conditional. And that sentence there is our conditional, it's justified by our culture, only if our culture is well impeccable. So following rule one and rule two, we've got P, we've got Q, and we've got that right hand symbol right in between, or is that the right arrow symbol, that graded end symbol right in between. And again, there's a space between the first proposition and the logical connective. There's a space between the logical connective and the second proposition. We want to make sure we get that right. So that's how we're going to symbolize a conditional. Now, keep in mind that conditionals can be written in a couple of different ways. So look at this. We've got, we've got to change around a little bit. Our culture is more impeccable if morality is justified by our cultural belief. All right. Now remember the difference between if on the one hand and only if on the other. If it's only if that indicates a consequent. That's what we saw last time. But in this case, we've merely got if, but that indicates an antecedent. Remember antecedents will not always be written first within the sentence. Okay. Now, since the order of the time of propositions has changed, their letter assignments has also changed. And remember, following rule one, the first time of proposition gets P. The second time of proposition gets Q. Right. Well, in this case, our culture is more than impeccable is now assigned P. Whereas in the example before, since that proposition occurred second, it was assigned Q. But this time it's assigned P. And the consequent now, morality, excuse me, the antecedent is morality is justified by our cultural belief. Since that occurs second, this time it's assigned Q. So instead of P greater than Q, right, instead of the P with that point Q, the order is reversed because of how they, you know, whether it's a P or Q, that's reversed now because of the order of their presentation within the argument. So conditionals are going to throw you as far as this is concerned. Right. Conditions are going to throw you whenever you got a disjunction, whenever you got a conjunction, you'll always be able to just put them in the order that they appear. That's not an issue. Conditions are going to be the weird ones. Which one is sufficient for the other? That matters with conditionals. Right. That matters. So you'll want to be careful with this when you be aware. So the first thing, right, when you see a conditional, find the antecedent, find the consequent. Whatever has an only if following after that, that's a consequent. Whatever has an if following it, that's the antecedent. Okay. So keep an eye out for that. Now most of these, now most, at least some of these arguments are not going to have atomic propositions as their components. And remember, I told you complex propositions can have complex propositions as their components. Now, when that happens, you need use parentheses to group together, you know, the smallest grouping, so to speak, or the smallest grouping of atomic propositions with logical connectives. So we'll use the parentheses to indicate the smallest grouping of atomic propositions connected by connectives. You know, two or more connected by connectives. So to use the parentheses, just so you know, we got, here they are. Use the shift button with the nine and the zero. Now the parentheses, the left hand parentheses should always be right up next to that proposition on the left. And that close parentheses should be right up next to the proposition on the right. So there shouldn't be a space between the parentheses and the propositions that it's enclosing. You might need to have a space outside the parentheses. That's, you know, that depends upon which connective you're using. But the parentheses should always be right up next to the propositions that it's enclosing. So we use these parentheses here for that. Okay. So here's a proposition. Morality is justified by cultural belief only if our culture is morally impeccable, and it is false as something needs to change. Okay. Now, immediately, you might be a little confused by this sentence, because it kind of looks like this, right? P, conditional, Q, ampersand, not R. Well, this is not a proper, this is not a proposition that expresses a logical, expresses a truth relation, right? We don't know if the truth relation is supposed to be indicated by the ampersand, or it's supposed to be indicated by the conditional. You know, we could have either one of these here. It could be a, this sentence could be a conditional, where the consequence is a conjunction, or the sentence could be a conjunction, where the first conjunct is a conditional, and the second conjunct is a negation. We've got two possibilities here. And even when you're reading, you might get confused as to which one it's supposed to be. You know, this is why grammar is, grammar punctuation is very important. So I want to show you two differences here. So the one on the left is where we have the conjunction, and the one on the right is where we have a conditional. Now, what's supposed to be the big difference between these two that indicates which one? Well, it's this little comma right here. That's the difference. That's what tells us whether we're dealing with a conjunction overall, or conditional overall. And there can be complex propositions within complex propositions. That's fine, right? I'm not complaining about that. This is a good thing. It, you know, it can be complicated after a while, but these are complex thought to express. But if you're going to express these properly, you must use proper punctuation. In this case, the comma makes all the difference. If the comma hadn't been there, this would be a conditional. This would be a conditional. But the comma is there. So we've got a conjunction. And this is how we properly express this complex sentence with complex, as a complex proposition with complex propositions as the conjuncts. So again, look, take, you know, take a close look at that, how the parentheses are used. That parentheses is right up next to the P for the open parentheses, and that closed parentheses is right up next to the Q. Don't have a space between between the parentheses and the conjunction and the proposition there. Okay. Now, this brings us to sequence. Now, sequence is when we take these formula representing the parentheses and the conclusion. And we use, we have just a single string of symbols to represent an entire argument. We're going to use this to express an entire argument. So with this, we got rule one, rule two, well, we're going to need further rules. Let rule three, list the conclusion last, always list the conclusion last in the sequence. And to indicate that you got a conclusion, we get two vertical bars and a space after the vertical bar, and then the conclusion. So for the vertical bars, again, on a standard quarter keyboard, you'll find them right here using the shift button, and that backwards leaning dash, I think it's called a back dash. Anyway, you find them here. That's the vertical bar that I'm talking about. That's the vertical bar I'm talking about. So let's write a sequence for this argument. Again, we got our example here. And that word so, that indicates our conclusion. And you remember we got morality is justified by cultural belief with the, is false that. So our conclusion is it is false that morality is justified by cultural belief. Now, if you remember, following rule one and rule two, when we saw that earlier, morality is justified by cultural, that was already given the truth, the letter p. So you still follow rule one for the assignment of letters and you assign them in order. And so we know that that gets minus not p as the conclusion. Okay, so that's the rule covering conclusions. We got a space. I'll explain, I'll say this again in a little bit, but say we got the last proposition for the premises, a space, two vertical bars, and then the conclusion. So the rule four lists the premises in order they appear in the argument and each is separated by comma. Okay, so we have the conclusion, we already brought that out. And we've got our first, we got our first premise here, morality is justified by cultural belief only if our culture is more than impeccable. Following rule one or rule two, that first atomic proposition got p, the second atomic proposition got q. We have them connected using our conditional sign that right pointing arrow, so to speak, or the greater than symbol, it's the greater than symbol. All right, so that's our first proposition. That's the first sentence, that's the first proposition, it gets a comma right after it, put that comma right up against the end of the first premise, but then a space after the comma. Second proposition, we've got that either or, so we know it's a disjunction, we've got the negations, so we know it's a disjunction on negations. Our culture is more than impeccable, that already got assigned q by rule one and rule two, so it's using the same proposition through there, and something needs to change in our culture, that was assigned r. So we had this not q minus q space, little v minus space minus r, and now we got the comma. So that's our second premise. This brings us to our third premise, however, something needs to change in our culture, that however, that's not a logical connective, it just helps us to understand what's going on within the sentence. So it's not actually symbolized by anything, something needs to change in our culture. Well, that was already assigned a letter by rule one and rule two, before it was a negated atomic proposition, now it's just the assertion of the proposition. All right, so there's no, it's just an atomic sentence. This premise here is just an atomic sentence. So it gets r, notice the last premise you don't get, there's not another comma, right, there's just a space between the last premise and the two vertical bars, then the space again, with the conclusion, with the conclusion. This is how your sequence should look, pay very close attention to how this is written, because the computer is going to be looking for exact entries for these answers. So don't do this, right, don't start squeezing in spaces, you know, don't forget the space between the comma and the premise, and don't forget the space between the conclusion, the premises, and the vertical bars. The vertical bars shouldn't have any spaces between them, but there should be a space on either side of the vertical bars. Especially don't do this, don't just type in a string of letters, the computer's not going to recognize what's going on, you have to separate these letters from each other, you have to separate the propositions from each other, and on the other hand, don't put in too many spaces, right? Don't just start putting out space between everything, no, take a look at that minus q, that's wrong, that negation symbol needs to be right up next to the proposition, the vertical bars, notice they have a space between them, don't do that, don't put a space between the vertical bars, okay? Just reiterate, this is what a proper entry looks like, and this is how you have a proper entry for this, okay? So let's take a look at a few practice exercises. So the first sort of exercise, you'll need to select the right formula given, you know, the question, right? So this question asks for a conjunction, which formula is a conjunction. Now this is pretty straightforward, this is not, you know, a mystery as to what's going on, you know, a conjunction is represented with an ampersand, and we see that with the third option, the bottom option is the greater than symbol that's for the conditional, the top is the lowercase v, that's a disjunction, the second for the top is the v, that's a disjunction, and the top is negation. So you just, you select the correct formula. Now, you know, the way to do this is you look for the connective, right? You look for the connective, and you remember, okay, conjunction is the ampersand, and you know, there you go, you see right there. Now, while that one's pretty straightforward, some of these can get a little complicated, especially when we have complex propositions within complex propositions. So you need to pay attention to the negations, right? And you need to pay attention to the parentheses. So looking at the bottom one, that bottom one there is not a negation, overall. There are negations in it, right? That's a complex proposition with negations in it, but overall it's not a negation. That bottom one is a conjunction of negations. Look at the second from the bottom. Overall, even though you have got the parentheses, right? And we've got negations, but overall that is a disjunction. That's a disjunction. Look at the main connective there in the middle, right? You can see that with this one, what really gives you the clue here is the parentheses for starters, right? So that parentheses gives you a complex proposition within the complex proposition. So that tells you that that should give you a clue as to what's the main operator overall. And so yeah, in this case, that's the disjunction. Go up on the second from the top. Overall, again, there's negations in there, but it's not a negation. And overall, it's a conditional. It's a conditional. So it's a conditional with negated and with a negated antecedent and negated consequent. The top one is actually the negation. It's the negation of a conditional, right? So it says it's not the case that if we think you it's a negation of a conditional, but the components of the conditional are not themselves negations, right? So the top one is a negation of a conditional. The second from the top is a conditional with negations. There's a difference there. So again, there's this top one here, that's actually the negation. Okay, now this sort of questions, a different sort of questions that are just merely identifying the kind of formula, right? Now you're given a sentence in English and you're supposed to find the formula that represents it. So you have to look for the connective here. Look for the right connective. So you have to look at the sentence itself. The animal is a llama, so the animal is a mammal. Well that word so there, that's the connective. The animal is a llama, that's a atomic proposition. The animal is a mammal, that's another atomic proposition. All right, so what sort of connective is so? Is it a disjunction? No, it's not, right? Oh, it's not. The connectives for disjunctions were or or unless, either or or unless. What is word so supposed to indicate? Well, it gives us a kind of inference, right? From the first one to the second, right? So is that a conditional? Yes, it is, right? So that's what the other three are, right? We got the other three, we got three conditionals here, okay. Well, we've got, you know, if P, we've got a conditional with P, greater than Q, right? There's a P conditional Q. We've got not P conditional, not Q, that's the third option, and then P conditional R. Which one is it? Well, are there, so we have to look for negations. Are there negations here? Well, you don't see any negations, right? The animal is a llama, the animal is a mammal. These are both assertions. These are both affirmative, okay. So we know it's not that third one from the bottom. Well, then we have P conditional Q and then P conditional R. Well, these are both conditionals, and they both kind of look right, you know, so what's supposed to be there for between them? Pay attention to rule one and rule two, right? For rule one, you assign P to the first term proposition Q to the second. Well, then that leaves out that bottom proposition, right? That, for that bottom one, R is assigned to the second proposition, but that breaks rule one. That breaks rule one. So you have to pay attention to when, pay attention to the assignments for the letters to ensure that you're following rule one and rule two. So what's that second one? That's the right one, P conditional Q, okay. Here's another one, right? What's the correct formula? I exist if I think. Hmm, what's the connective? Well, the connective is if. Now, this should immediately send up an alert, right? We've got a conditional here, but we know there's an issue between if and only if, right? Well, if it's only if, then that only if indicates the consequence. But here we just have if, and if we just have if that indicates an antecedent, okay. So take a look at our options here, not P, look at the top one, if not P, then not Q. Well, we're going to roll that one out because there's no negations within this sentence. We've got if P then Q, well, that's a conditional, there's no negations that already looks right. We've got if P then R, so again another conditional, but no negations that also looks right, and the last one if Q then P. Oh boy, yeah, what are we supposed to do here? Now we've got three that look right. We'll take a look at the second from the bottom. We already talked about this, right? Following rule one, that R is out of place, right? And there shouldn't be an R, should be a Q. So then we have if P then Q, and then if Q then P, well, it looks like then it should be if P then Q. But remember, if indicates the antecedent, right? I think it's the antecedent and following rule one, that will be assigned Q, right? I think in the proposition that word if there indicates the antecedent, I think it's the antecedent. So that's given Q and then I exist is P. And so that's the bottom one, that Q conditional P. That's the right formula for this sentence. Be careful when you're translating. Watch the placement of letters in the conditionals. Watch if and only if, right? You got to pay attention to which one's given to which, if indicates the antecedent, only if indicates the consequence. So again, it looks like it might be between these two, or even that third from the bottom one, but it's only this one. It's a Q conditional P. That's the correct formula. All right, looking at this one, notice we've got Q conditional P, right? So for the others, we had translating from a sentence to the formula. Now we have a formula to a sentence, okay? Now we have a formula to a sentence. So what do you think we should do? Well, take a look at the first things first, take a look at the connective. The connective is a conditional. Well, the first option is or, well, that's a disjunction. So that's not the one. The second option is, you know, if then those are the those are the connectives there. Okay, well, that's a candidate. The third option, the figure sides are parallel. If the figure is a square, that's also a conditional. And then the last one, the figure squared is a parallel and the figure is a square. Well, that's a conjunction. So that's the choice between the second and the third. All right. Well, how do we distinguish between them? Well, pay attention to the order of the letters in the sentence. That should tell you something. The, remember the order, which is supposed to do is go from the sentence to the letters, you're supposed to sign the first atomic proposition, the P, the second atomic proposition, Q. So already, since we have Q right there, what we're told is, what we know from our rules is, the antecedent is the second proposition, second atomic proposition. Well, that happens in the third one. We've got that if the square, the figure is the square, that's the antecedent, it's indicated by if, and it's the second atomic proposition. So that's why it gets if Q then P. All right. So now we have a complex proposition of complex propositions. Overall, what sort of formula is this? Is this a disjunction? No, there's no disjunction conditional. No, just no conditional. We've got negations here, but is this overall a negation? No, no, this is overall, this is not a negation. This is a conjunction overall, it's a conjunction of negations. All right. So let's take a look at the sentences. The first one says either or, right, well, so that's a disjunction, we figure that out, so that's not it. The second proposition, the connective is if then, so that's a conditional, well, that's not what we're looking for. The third one is either or. Okay, so that's a disjunction. Well, that's not what we're looking for. We'll find the last one candidate left does not win the election and candidate right does not win the election. That's the conditional of negations. Be careful when you look through, you want to make sure you pay attention to negations. You want to make sure you pay attention to the to the connectors for disjunction, conjunction and conditional. Make sure you're matching up the right ones. So for the next sort of problem, you're given an argument and you're supposed to assign the atomic propositions. Now we've been rather helpful here and I've indicated, right? So we have that. So just looking at all truth is relative, but that's our first atomic proposition. I've been helpful here and already telling you where the atomic propositions are. So you just have to start assigning the letters according to rules one and rule two. So you'll hit that select button there on the screen and it'll give you a little pulldown menu and then you select the proper assignments following rule one and rule two. So the first one all truth is relative. That's the first proposition. It gets P. We had to assign that P. So you select which letter to use and then for keeping in mind for rule two, right? So I have this atomic proposition. If there's some absolute truth while following rule one, it gets Q. But you have to look out for the rest of the argument. Notice that proposition also pops, atomic proposition also pops up down here near the bottom. So it needs to get Q two. So you can't just go through the list of first one P, second one Q, third one R, fourth one S. In fact, if you notice there's, you know, this P through U for the pulldown, you may not use all of these. It was one or two where you're going to use all of them. But for some of them, you're not going to use all of the letters. So you're going to need to pay attention to rule one and rule two in order to assign the proper letters. So for the, so this is a similar sort of problem, except in this case, instead of a pulldown menu, you type in the letters, right? You type in the letters. So you look for the atomic propositions. And in this case, right, I've got the blanks here. So you know that that's the atomic proposition. I've helped you out with this. You don't, you know, you don't need to discern the difference between the time of proposition and the complex one. But you need to pay attention to which atomic proposition you're dealing with, because some of these might pop up, you know, more than once. So for instance, that first atomic proposition, either person is either a person, excuse me, a person is pursuing a good life. That's the atomic proposition. Well, that pops up again, several times, right? If you notice in that second sentence, there it is. A person is pursuing a good life. Well, that needs to get, so the first time you see it, it gets a P. The second time you see that a person is pursuing a good life, like it's a P there too, following rule one and rule two. So you need to pay attention to where those, if it gets a letter, one point on the argument needs to get the same letter throughout the rest. And in this case, as I said, you are typing in the letter. You're typing in the letter. So you're going to type it directly into the blank. Okay. Make sure it's capitalized. Make sure it's just the letter. Don't type anything else besides that. So this question, sort of problem, you have to put it, you have to type in the P, the Q, the R, and so on. For the next kind of problem, you have to type in the whole formula. Some of these will just have one formula. Some of these will have as many as three. This one actually is three. So it's not just notice a change in the instructions, right? You know, symbolize the following proposition, not just putting in the letters, you're symbolizing the whole formula. So the whole sentence. So that first sentence, if one talks about nothing, then either nothing is a subject or nothing is a predicate. Now it's kind of fun about this case. Right away. You got to watch out for parentheses when necessary. You got to watch out for those parentheses. So in this case, we got that either or happening right after, right after the then with the consequent for the conditional. So you got that either or, yeah, that comma is there and you're like, oh, wow, that's separate. No, it doesn't, right? Because that either is contained, just immediately within the consequent. The either or they always have to go together like that. So this is a conditional, right? This is a conditional with a disjunction in the consequent, right? So it's going to look like that. You got the conditional with the with the disjunction in the consequent. Okay. So make sure you pay attention to the parentheses when necessary. That's that'll pop up. And not always, right? Look at that second sentence. If nothing is a subject, then one can describe nothing. That's just a straight up conditional. There's no complex propositions within the conditional. Okay. The last kind of problem, you're going to need to put in the entire sequent. And so this is going to require pretty much all the skills that we've been developing so far, right? We've had to, you know, we have to identify the premise and the conclusion. You have to assign atomic letters to the you have to identify the atomic propositions for the complex. You have to assign letters to the atomic propositions using rule one and rule two. And this one you have to deal with real rules three and rule four, right? Rule three and rule four. Remember, rule three, you got to put that conclusion first. And then you put in the premises in order. Now, this one's kind of straightforward, right? Because we see that as far as identifying the conclusion, we got that therefore, if we're sometimes mistakenly perceptually, that indicates the conclusion. And so, you know, the rest of these sentences in this argument are premises. And you'll type them in that box that you'll see right there. Here's another example. And this one is, I'm going to highlight this one in particular because this can trip you up. Rule three says, list the conclusion last. All right. In the sequence, list the conclusion last in the sequence. Well, if you're reading this, say the first sentence, either a person is pursuing a life of happiness or a person is pursuing a life of misery. Four, either a person, so that four indicates a set of premises that follows. So that first sentence there, that's the conclusion. And that's the conclusion. Following rule three, you'll list the conclusion first, a space before, you have a space, then the two vertical lines, another, you have two vertical lines, then another space, then the conclusion, the conclusion itself is a disjunction. Following rule one and rule two, it's the first atomic proposition gets that P, the second atomic proposition gets that Q. So it's P or Q. And then you'll follow the rest of the rules, you provide the premises in order separated by comma. Okay, let's take a look at this next one. It's false that one could talk about nothing. If one could talk about nothing, then either nothing is a subject or nothing is a predicate. If nothing is a subject, the one could describe nothing. And nothing is a predicate, the one could describe, can be described as nothing. It's impossible to describe nothing. And it's impossible to describe something as nothing. This is difficult. We have no indicator words. We have no indicator words telling us which one is a conclusion. Well, try to look at the under, try to comprehend the meanings of the propositions here. Right? How is, how is the reasoning progressing? Now the first sentence is negation. Right? So following rule one, it gets assigned P and it's the negation, not P. The second sentence has that same atomic proposition, except in this case, it's not negation. Right? The first atomic proposition, sorry, the first complex proposition, the first sentence, it's false that one could talk about nothing. One could talk about nothing is the atomic proposition. That's P. So that's not P is that total complex proposition there. Look at the sentences. If one could talk, you know, if one can talk about nothing, it's like we just completely ignore the negation to begin with. And it goes into this line of reasoning where at the end, this is, well, by the way, if we assume that we could talk about nothing, then we reach these impossible conclusions. Well, if we reach a possible conclusion, that first assumption has to be false. This is a difficult one, but that first sentence again. In this case, it's also the conclusion. This isn't always going to happen, but sometimes it will happen. Okay, so when we are typing out the premises for this argument, so we got our conclusion, we're typing out the premise, it kind of gets cut off in the box, but that's all right. Don't worry about it. Just make sure you type it in there correctly. It should be fine. But you notice we've got several complex, we've got complex propositions within complex propositions. We've got complex, if one could talk about nothing, then either, that tells us that the consequence is a disjunction. The second one, that the subject is another one, that's a straight up conditional. So when you're translating, you've got to spot the connectives really fast. That helps identify the atomic propositions. That helps you rule one, identifying the atomic propositions, making sure you have the same one assigned to follow rule two, and help you identify the premises in the conclusion. The connectives are really key for figuring that part out. This is just yet another example, right? So this is what a completed, oh, I'm sorry. This is not a completed example. Sorry, I want to tell you, watch out for a couple of things. Don't leave your sequence with a comma separating the last premise from the double vertical bars. Your last premise should not have any commas. Don't leave an incomplete sequence. If you do either one of these things, you're not going to get any credit, the computer is programmed to recognize the sequence. It can't recognize meaning, it can only recognize a string of letters and symbols, right? So you have to type it in precisely following all four rules that we've been given. If you miss something in there, it's going to count the whole thing wrong. This is kind of another tricky one. That what's within quotation marks, that's itself not an atomic proposition. That believe it or not, that whole first sentence is an atomic proposition. Or excuse me, it's a complex, sorry, it's a complex, right, with negation, right? The atomic proposition would be there is empirical content for the claim all knowledge is empirical. That would be the atomic proposition, right? That says there is this thing. That's the atomic, since it got the no in there, that makes it an negation. So you have to be careful to spot the difference between a sentence that's mentioned within a sentence and the atomic proposition itself, right? Sometimes a sentence with mention within a sentence can be an atomic proposition. You have to pay attention to the meaning of the sentence. Make sure that when you type in your sequence, you have the proper spaces. This is incorrect. It will not work out well. If you do this, make sure you put you have the all the premises and make sure you have the premises and the conclusion. Otherwise, it won't count. All right, so that's kind of a rundown of all the kinds of problems we have for this chapter. Good luck with it. If you need to come by my office and talk about this, I'm more than welcome to see you.