Problem 1.
The following predicate logic formula is invalid:
∀x,∃y.P(x, y) → ∃y,∀x. P(x, y)
Which of the following are counter models for it?
1. The predicate P(x, y) = 'y.x = 1' where the domain of discourse is Q.
2. The predicate P(x, y) = 'y < x' where the domain of discourse is R.
3. The predicate P(x, y) = 'y.x = 2' where the domain of discourse is R
without 0.
4. The predicate P(x, y) = 'yxy = x' where the domain of discourse is the
set of all binary strings, including the empty string.