Question

6) What is the truth value of each of the following wff in the interpretation where the domain consists of integers? a. ("x)(x² > 0) _______ b. ($x)($y)(x² > y) ______ c. ("x)("y)[(x < y) → (y > x)] ______

Answer 1

There exists and For all quantifiers are not clear in the question so, I'm answering each for both possibilities.

a)

This TRUE as say when x=1 then 1>0.

This is FALSE as when x=0 then 0 is not greater than 0.

b)

This is FALSE as when say x=1 and y=2 then, 1 is not greater than 2.

This is TRUE as when say x= 2 and y=1 then 4>1.

c)

This is TRUE as say when x=1 and y=2 then it holds.

This is always TRUE.