Question

The statement among the following that is a tautology is :

• A. $A \wedge (A \vee B)$
• B. $A \vee (A \wedge B)$
• C. $[ A \wedge (A \to B) ] \to B$
• D. $B \to [ A \wedge (A \to B) ]$

Hint:

The statement $[ A \wedge (A \to B) ] \to B$ is a fundamental rule of logic known as "Modus Ponens."

Answer 1

The Correct Option is C

Step 1: Use the truth table or logic laws.
Step 2: $[ A \wedge (\sim A \vee B) ] \to B \equiv [ (A \wedge \sim A) \vee (A \wedge B) ] \to B$.
Step 3: $[ False \vee (A \wedge B) ] \to B \equiv (A \wedge B) \to B$.
Step 4: $(A \wedge B) \to B$ is always true (Tautology), as if $A$ and $B$ are true, $B$ is certainly true.