Okay, so let's see how we use a truth table to analyze an argument to see if it's valid or invalid. So I've made up an argument here. If there is cream, then I will drink coffee. If there is a donut, then I will drink coffee. There is no cream and there is a donut. Therefore, remember the signs are therefore, I drink coffee. Okay, so here are all of my premises. Here is my conclusion. And remember, it will be valid if I have a totology in my final column. First thing we need to do is do a translation. I need to get all of these statements condensed down to p's, q's, and r's. So let's go ahead and assign the... So how about if there is cream, that's going to be my p, and i will drink coffee, can be my q. On the only other statement I have in there is about a donut. So there is a donut, can be my r. So let's do a little translation. I'm going to try to squeeze it in right here so that we can be looking at it. Grab my blue. So that first line, if there is cream, then I will drink coffee. So symbolically that looks like this, if p then q. If there is a donut, then I will drink coffee. So that's if r, then right, q is my coffee statement. There is no cream, so not p, and there is a donut, that was my r. And p and r, therefore i drink coffee, that's my q. So this is going to be a tight squeeze, I just used up all of my space. That's okay, we are going to work around it. So here is my truth table starting. I have my p column, so remember I have three statements, so I need eight rows. P goes four, truth, and four, false, q alternates by twos, are alternates every other. And now I need to build each of my lines in my, um, from a C statements, so if p then q. Let's try to make these short. So if p then q, so I'm going to run my fingers down the p and q column, if true then true is true, if true then true is true, if true then false, remember this is our only false, if then statement. If true then false, false, if false then doesn't matter, that's always the true. So these last ones, my antecedent is false, so it doesn't matter, I'm always true coming out. So there is if p then q. So now let's do, um, if r then q. Okay, I'm going to have to read right to left, so this is going to be harder, but here we go, we'll hold them here. So if r then q, if true then true, that's true. If false then it doesn't matter. If true then false is false. If false then it doesn't matter. If true then true, that's true as well. If false then true, that's true. If true then false, that's my only false situation. If false then false, that's also true. Last line on my premises, it's a not p and r. Okay, I don't have a not p column, so let me sneak in a not p column real quick. Right, that just changes everything that was true, it will false, and everything that was false to a true. So four falsees, trying to line up as best I can, then four truths. And now I'm going to end that column, so not p column and r. I have my fingers again, so not p and r. For and to be true I need two truths. So I have one false, so that's false. I have two falsees, that's false. One false, that's false. And false. And here's a true and a false and a true and a false. Okay, so they're all my premises. So the next thing we do is we AND all of these together. So I'm going to do an AND with all of these, this and this and this. All three have to be true to get true in my AND column. So I'm just going to do a big AND, how about if I just label it premises? Promises. Otherwise it's too long to write all of these with ANDs in between them. Okay, all right, so oh my gosh, where's my p? Maybe I better highlight those, let's see, so it's this one. One are then q and not p and r. So it's those three, so three fingers. I need all three truths to be true. So as soon as I have a false, then my AND here is going to be a false. Wind paper is really a good idea on these, by the way. Oh, there I've got a true. My first true down in the fifth spot. As soon as I have one false, I know that this is a false. Okay, so there's the AND for all of my premises. So the way the argument works, oh my gosh, I'm going to fit it in. This is totally cool. So as we do all of our ANDed premises, as my IF, then my conclusion. So all of this, my ANDed, all the premises column, is the IF part, the antecedent. IF, then my conclusion. Okay, so I'm looking for all truths down here. As soon as it starts looking good, then I can say, yeah, it's about. Okay, so my AND is my IF, over all the way over here to my q. IF false, and remember if the antecedent is false, it doesn't matter what the conclusion is. IF false, then, that's a true statement. IF false, then, that's a true statement. That's a true statement. Right, I'm not even looking over to see what q is because my premise part is false. IF false, then, it doesn't matter. Oh, here I have to check. IF true, then true. That's good. You can keep that one. IF false, then, IF false, then, and IF false, then, I was only had one true in my ANDed premises. And that went to an IF true, then true, so that worked. All truths in this column, remember that's called a tautology. Tautology. And when we get that in our final column, we say that the argument is valid.