Question

The statement A → (B → A) is equivalent to :

• A. A → (A ∧ B)
• B. A → (A ∨ B)
• C. A → (A ↔ B)
• D. A → (A ⇔ B)

Hint:

Use the identity $P \to Q \equiv \sim P \vee Q$ to simplify logical implications quickly.

Answer 1

The Correct Option is B

Step 1: $A \to (B \to A) \equiv \sim A \vee (\sim B \vee A) \equiv (\sim A \vee A) \vee \sim B \equiv T \vee \sim B \equiv T$.
Step 2: $A \to (A \vee B) \equiv \sim A \vee (A \vee B) \equiv (\sim A \vee A) \vee B \equiv T \vee B \equiv T$.
Step 3: Since both are tautologies, they are equivalent.