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2 Write the statement p 2 T) V Iwithout buzsn the connectives and...

Question

2 Write the statement p 2 T) V Iwithout buzsn the connectives and

2 Write the statement p 2 T) V Iwithout buzsn the connectives and



Answers

Write the assumption you would make to start an indirect proof of each statement. $$\overline{P Q} \cong \overline{S T}$$

All right, This statement is true By # three of the chart this is one of the loss of um identity loss, this one of the only loss.

I also asked to write the negation of the statement. Let's let P be. If you ask me, thank you be I will do it. So then, if we negates, P implies Q. That's equivalent to pee and navigation of cute. So that is we have P, which is, if you ask me and in our connective on and an investigation off Q, which is I will not do it.

Mhm. For this problem, we'd like to determine whether or not this implication is sure, Boss and were given that T is always true because it's a it's a tautology, and because he's always true, we see here that our conclusion, it's always true. The T. Here Now, it turns out that the hypothesis is also true because it has to be there and it's a war. But regardless of the hypothesis, this entire sentence, it's true sense. Its conclusion is true.

For this problem we are given that T. Is a tautology which means that T. Is always true. For example, he might be something like zero equals zero. Doesn't have to be that example. But it's just a statement that's always true no matter what. And we want to find the truth value of the proposition T. If and only P. Or T. Now there's many ways to do this. One way. It might be. The simplest is to just use the truth table. But when you do this, you have to see that because he's a tautology, it's always true. So your only options for a little T. Should be true regardless of P. S. Shoe revolves. Yeah. Okay. Next up we C. P. Or T. Down here. So if I take A. Or here if I have at least one true then the ore is true. And then we're looking at he if and only if so remember if and only if B. Is true if you have two cases A and B are both true or they're both balls. In other words, A and B have to have the same truth value. And sure enough here, we're looking at the second column and the third column, and we can see here that in each case they have the same truth value. And we conclude because we see that the proposition were interested in is always true. That's the answer to the proposition. It's true and this is regardless of whether or not peace itself is true or false.


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