Question

Q(x,y) is a propositional function and the domain for the variables x & y is: {1,2,3}.

Assume Q(1,3), Q(2,1), Q(2,2), Q(2,3), Q(3,1), Q(3,2) are true, and Q(x,y) is false otherwise.

Find which statements are true.

1. ∀yƎx(Q(x,y)->Q(y,x))

2. ¬(ƎxƎy(Q(x,y)/\¬Q(y,x)))

3. ∀yƎx(Q(x,y) /\ y>=x)

Answer 1

Statement 1 is true whereas statement 2 and 3 are not true. I have explained everything in the solution.