Question

Prove each of the following assertions:

a. α |= β if and only if the sentence (α ⇒ β) is valid.

b. α is valid if and only if True |= α.

c. For any α, False |= α.

d. α ≡ β if and only if the sentence (α ⇔ β) is valid.

e. α |= β if and only if the sentence (α ∧ ￢β) is unsatisfiable.

Answer 1