# Thread: Sets and Logic, Conditional Propositions, and Nested Qualifiers

1. ## Sets and Logic, Conditional Propositions, and Nested Qualifiers

Write truth table.
22. p ^ ¬q.

27. Let p = true , q = false, r = unknown. Tell whether each proposition is true, false, or unknown.

(p ^ r) <--> r

Doing truth table, I got that p ^ r is unknown because r changes what it is.
R is unknown, so we have 2 unknown sides.

However, the answer is True.

Let P(x,y) be the propositional function x >= y. The domain of discourse is Z+ x Z+ .
Tell whether each proposition in Exercise 36 is true or false.

36. ∀x∀y P(x,y)

I don't understand how to start.

Thanks!

2. You shouldn't post so many problems in one thread.

22. What did you try?

27. You can prove that the statement is true. Basically, assume p is true, and go from there.

35, 36. I'm puzzled. Those look like the same expressions.

3. 22. I figured it out.

27. Ohhh. Got it. Thanks

36,35 - I messed up. It's just one question. 36. I'll edit it.

4. 36. Ok, so suppose for a minute that it's false. If you were going to try to prove that it was false, how do you think you could go about it? You've got two universal quantifiers there. That's important.