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1. ⇒ (MHT CET 2023 9th May Evening Shift )

Let $p, q, r$ be three statements, then $[p \to (q \to r)] \leftrightarrow [(p \land q) \to r]$ is

A. equivalent to $p \leftrightarrow q$ .

B. contingency.

C. tautology.

D. contradiction.

Correct answer option is (C)

Given statement,

$\begin{aligned} [p \to (q \to r)] & \leftrightarrow [(p \land q) \to r] \\ p \to (q \to r) & \equiv\sim p \lor (q \to r) \\ \equiv\sim p \lor (\sim q \lor r) \\ \equiv [(\sim p) \lor (- q)] \lor r \dots [Associative law] \\ \equiv\sim (p \land q) \lor r \dots [De'morgans law] \\ \equiv p \land q \to r \end{aligned}$

$∴$ Given statement is tautology.

⇒ Mathematical Logic