Question

Use laws of logical equivalence (not truth tables) to prove that the following sentences

are logically equivalent.

(A & ~B) V (A & ~C)
~~A &~ (B & C)

Answer 1

See below

Explanation:

Refer to the attachment.

Given:

(A ∧∼B) ∨ (A ∧ ∼C)

Solving steps:

≡A∧(∼B∨∼C). . . . . Distributive Law

≡A∧∼(B∧C). . . . . . De Morgan's Law

≡∼(∼A)∧∼(B∧C). . . . . . Double Negation Law

Hence,

(A ∧∼B) ∨ (A ∧ ∼C)≡∼(∼A)∧∼(B∧C) [Proven]