Prove each of the following assertions: a. is valid if and only if True | =

Prove each of the following assertions:

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

b. For any a, False | = α.

c. α | = β if and only if the sentence (α → β) is valid.

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 un-satisfiable