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!