Question

The statement among the following that is a tautology is ______.

विकल्प

• A ∧ (A ∨ B)

• B→[A ∧ (A→B)]

• A ∨ (A ∧ B)

• [A ∧ (A→B)]→B

Answer 1

The statement among the following that is a tautology is [A ∧ (A→B)]→B.

Explanation:

Tautology is the case where each value is true.

1. A ∧ (A ∨ B) ≡ T or F

2. ⇒ B → [A ∧ (A → B)]

≡ B→[A ∧ (∼ A ∨ B)]

≡ B → F

≡ T or F

3. ⇒ A ∨ (A ∧ B) ≡ T or F

4. [A ∧ (∼ A → B)] → B

⇒ [(A ∧ ∼ A) ∨ (A ∧ B) → B

= (A ∧ B) → B

= (∼ A ∨ ∼ B) ∨ B

= T