Question: Prove each of the following assertions: a. is valid if and only if True . b. For any , False . c.

Prove each of the following assertions:

a. α is valid if and only if True ⊨ α.

b. For any α, 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 unsatisfiable.

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