Is the following true or false? (a) ∀x∃y.P (x, y) ≡∀y∃x.P (x, y).

Is the following true or false? (a) ∀x∃y.P (x, y) ≡∀y∃x.P (x, y).

March 18, 2022

Is the following true or false?
(a) ∀x∃y.P (x, y) ≡∀y∃x.P (x, y).
(b) ∀x(P (x) ∨Q(x)) ≡∀x(Q(x) ∨P (x)).
(c) ∃x.(P (x) ∧Q(x)) ≡(∃x.P (x)) ∧(∃x.Q(x)).

Solution:
Is the following true or false?(a) ∀x∃y.P (x, y) ≡∀y∃x.P (x, y).

Is the following true or false?(a) ∀x∃y.P (x, y) ≡∀y∃x.P (x, y).



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