 In this video I'm going to talk about related conditionals. Basically what I'm going to talk about is a couple of vocabulary words that go along with conditional statement. We're going to talk about converse, inverse, and contrapositive of a conditional statement. That goes with a little bit of notation and writing out of these sentences. So here we go. Conditional statement is your traditional, conditional statement is an if-then statement. Here's your if-then statements, your hypothesis, and your conclusion. Now what we have here is we have some symbols that help us with this. So p, then q, that's kind of what this symbol means. So I have a sentence that goes with this to help us with this p, then q. If the area of a square is 9 meters squared, then the sides are 3 meters. So now we're not too worried about the validity of the statement, we don't care if it's right or wrong, we're just looking to rewrite it as a converse in this slide anyway. So what we're doing is we're looking at the converse. If the area of a square is 9 meters squared, that's the p part of this symbol. It's the hypothesis, it's the if part. So what I can do, what I should do, is move this, got to like the computers, oh come on now, move this right here. Okay, if is the p part of the statement, then is the q part. So the hypothesis is the p and the conclusion is the q part. So the converse, what we do is we actually say if q, then p. So what we do is we kind of flip-flop everything. So what we're going to do is we're going to take the hypothesis and the conclusion and we're going to flip them. Now this sounds easy, but you got to remember when you write these sentences, they still have to flow, they still have to make sense in English. You just can't take blocks of text and move them around. You have to make sure that the sentence flows and it makes sense. All right, so if the area of a square is 9 meters squared, then the sides are 3 meters. Okay, so now what I'm going to do is I'm going to take this part, the sides are 3 meters, that's going to be my hypothesis. But I can't just say the sides are 3 meters, the sides of what? This is the tail end of the sentence where we've already identified what the subject is. So I just can't say if the sides are 3 meters, that doesn't make sense. I have to say if, I have to actually state what I'm talking about. If the sides of a square are 3 meters. Okay, so notice what I did there, the sides are 3 meters is right there. The sides are 3 meters, but the sides of what? Of a square, so this of a square part. I actually kept that in the beginning of my sentence. Because if I took that out, it wouldn't make any sense. I wouldn't know what I was talking about. If the sides of a square are 3 meters. So I have to keep that in there so I know what I'm actually talking about. Now I can do the conditional part of my statement, I can do the conclusion part of my statement. Then the area is going to be 9 meters squared. Then the area is 9 meters squared. Okay, so notice what I did there, I didn't just this of the square, I didn't put that in there. I just took this hypothesis part and I put it at the end because this is a converse. If p then q, the converse is if q then p. So I'm flipping around everything, but notice when I flipped around everything, the of the square part, that stayed at the beginning of my sentence, I need that there so I know what I'm talking about. If I put that at the end of the sentence, it was too late. If I put it at the end of the sentence, I have no idea what I'm talking about until I get to the very end of the sentence. That makes no sense. So leave that at the beginning of the sentence. You got to do a little bit of thinking. You got to use a little bit of your English skills here to make sure that these sentences make sense when you write converses, inverses, contrapositives and all that. So that's a conditional statement, your traditional if-then statement, and then also a converse. So on this next slide here, what I have is an inverse and a contrapositive. Now, using the same example, if the area of a square is nine meters squared, then the sides are three meters. So now I'm going to write the inverse. The inverse, well, the inverse is the not statement. The inverse is kind of the opposite statement. So what these little twills here, what these little symbols here, is means not, not, okay? So not p, then not q. Basically what it is, is I want to say the first sentence is not true, and then I want to say the second part of the sentence is not true. It's actually relatively simple. I just want to put not somewhere in there so that it basically makes that part of the sentence not true, okay? So if the area of a square is nine meters squared, so all I need to do is say if the area of a square is not nine meters squared. That's going to be the first part of my inverse. If the area, notice I'm not switching anything around this time. Everything's staying where it's at. p is in front, q is in behind. Everything's staying where it's at. But now these twill, these little symbols mean not, okay? So if the area of a square is not nine meters squared, then the sides are not three meters, okay? Now as you read through that sentence, you might think to yourself, whoa, wait a minute, but is that true? Is that not true? That's not what we're worried about right now. We're not worried about whether it is true or not true. We're just writing them down. We're not worried about the validity. We're not worried about if it's true or false. We're just worried about writing it down, okay? So that's inverse, basically adding a not to the sentence, and now we're gonna write the contrapositive. Contrapositive, you notice the q and the p have switched places, and now we're also writing the not. Contrapositive is a combination of your converse and of your inverse. It's combining both of them, combining both of them. So now we've looked at all the different ways to kind of switch up a conditional statement. You can flip, you can flip the, the, forgot to work. You can flip the hypothesis in the conclusion. You can flip them around. You can say the opposite of what they are, and you can flip them around and say the opposite of what they are. That's what we're gonna do with the contrapositive. Okay, so the contrapositive, so I'm gonna use a lot of what I said previously. So if, now I'm gonna talk about this part, if the sides of a square are not three meters, if the sides of a square are not three meters, then, now I'm gonna write the beginning part here, then, then the area is not nine meters squared. Then the area is not nine meters squared. Okay, so there is our contrapositive. So to kind of recap a little bit, let's summarize this a little bit. We have three, we have three vocab words. I've kind of went over here. Conditional statement is your if, then statement. A converse is your, basically what you do is you take the hypothesis and the conclusion and you switch them around. Your inverse is when you take the, not, you don't switch them around, but what you do is you take the opposite of what you're saying. So basically you're adding this word not, you're adding this word not into your sentence, into your conditional statement. And then the contrapositive is a combination of both your converse and your inverse. Your contrapositive is you're not only saying the opposite, but you're also switching them around. Okay, if the sides of a square are not three meters, then the area is not nine meters squared. Okay, so that's kind of a summary of everything that I just went over. So those are, those are the related, what we call the related conditionals. I hope this, I hope this video was informative.