 In the previous video, we talked about set compliments and how it represents not. We wanna do now the Boolean logic equivalent of that. And that's the idea of a negation. A negation is a statement expressed in the idea that something is not true. So we would represent this often with this sort of like square bracket right there. Some people use like a little twiddle. That's okay as well. So negate the following statements here. So the, we'll take the statement P. P is the statement that the high definition screen is included in the price of the computer. It's a statement, it's either true or false and honestly, depending on the computer you're buying and the store you're buying from, it might be sometimes true, sometimes false. We need more information, but it is a statement that's either true or false. The negation would be to put in the word not. So not P means the high definition screen is not included in the price of your computer. That's what it means to negate things. Here's another statement, B. The blue whale is the largest living animal. Okay, that's a true or false statement. Is it true, is it false? I mean, I think it's true. I'm certainly not a marine biologist or anything like that, but I'm pretty sure the blue whale is the largest animal out there. Not B would mean that the blue whale is not the largest living animal, okay? These are both statements. Negation just switches by adding the word not in there. Now, as we worked with conjunctions and disjunctions before, it's important to see how this operation works with the two values that a statement can take on. If you are not true, that means you're false. And if you're not false, that means you're true. So the negation is like a light switch. You toggle on, off, on, off. True, false, true, false. It switches between them. And so it's very important as us, as budding Legiotians, to be able to build and negate statements. So consider the following here and we're gonna do this with some compound statements because it gets more complicated. Take two statements here. P, as a primitive statement, the tenant pays the utilities. And D, a $150 deposit is required. So these might be like conditions that a tenant would sign when they sign a lease for a new apartment or something. Oh, you're responsible for paying the water utilities. Oh, there's a $150 pet deposit or something like that. These are reasonable conditions you can have here. So can we combine them together? So express the statement, it is not true that the tenant pays utilities and a $150 deposit is required. So I want you to notice this right here is our primitive statement P. This is our primitive statement D. This is an and, so that puts it together with a conjunction. And then it's not true that, that's a not statement. That's what all these things are. We have to make sure we combine them together using parentheses because order of operations matter. This statement would be not P and D right there, which is not the same thing as not P and D. You have to be very careful here. And this is not the same thing as not P and not D. You have to be very careful. This not applies to the whole statement, the whole following statement, which itself is a conjunction. It's a compound statement there. So the correct symbolic way to write this will be not P and D. Well, what about this one right here? Not P and not D. And that situation, you would get something like the tenant does not pay utilities and a $150 deposit is not required. Man, I would wanna sign that lease. Those are pretty nice conditions there, but maybe you know, maybe you're renting the mother-in-law suite to dear old grandma or something in a house. There's no requirements for her, right? So that's the difference here. So these are not the same statement, right? And we'll dig into this a little bit more into the future, of course. That's always the case. We hint toward things and then we come back to them later. I wanna do another example before I end this video about negation, all right? Which is the logic version of compliments. So let's take two different primitive statements this time. Let's take H, we will build more hybrid cars. And F, we will use more foreign oils. So these might be things that like a politician might say, with regard to climate policy or something like that. We will build more cars. We will use more foreign oil. Well, typically the same person's not gonna say both of these things, right? So consider the following statement. We will not build more hybrid cars or we will use more foreign oil. So maybe this would be someone who basically is not supporting a policy to cut back on climate change. They might say something like this. It's like, I don't care about hybrid cars. Let's use foreign oil, it's the best. They might say something like this, right? And so let's put this together. Now notice this right here, build more cars. That's our H, but there's also a not here. So we have some type of not going on there. There's an or and we will use more foreign oil. That looks like F right there. So putting this together, we end up with the statement not H or F. Now we have to be careful that this is not the same thing as not H or F. That is a different statement. So you have to be careful to represent these correctly. Let's actually consider that one here. What would not H or F come out to be? Now, when it comes to these logical statements, I don't necessarily want you to worry about making the language pretty. Just say it as it literally is. And so because the not is in front of a compound statement, you can get away with the following trick. It is not true that and then you put a colon. So the next statement is what we're negating, right? Again, you can make more pretty language, but we'll worry about that later. So the next statement is H or F. So H is we will build more hybrid cars. And then we have a disjunction. So we get or and then we get F. We will use more foreign oil. I guess I should have a capital up there. So that is the negation of that sentence. It's kind of an awkward way to say it, but at this point of the game, we're not gonna worry about that. Later on, we'll talk about how different logical statements can be logically equivalent. And therefore we could rewrite this statement using a much more elegant language, but that'll be using the logical version of De Morgan's Laws, which we'll talk about that some other time.