In the questions below P(x,y) means “x and y are real numbers such that x + 2y = 5”.

Question

a) Determine whether the statement ∃x∀yP(x,y) is true.

b) Negate the statement ∃x∀yP(x,y).

Answer 1

a) Choose any x, you can easily find a y that makes P(x,y) false.

b) ∃ and ∀ switch with negation;
∀x∃y ~P(x,y)