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.
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.