First slide

Introduction to mathematical reasoning

Question

Let $p, q, r$ be three statements.
Statement-1: $p \leftrightarrow q \equiv (p \to q) \land (~ q \lor p)$ is a tautology.
Statement-2: $p \lor q \to r \equiv (p \to r) \land (q \to r)$ is a tautology.

Easy

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C

STATEMENT-1 is True, STATEMENT-2 is False
D

STATEMENT-1 is False, STATEMENT-2 is True

Solution

$\begin{array}{l} p \leftrightarrow q \equiv (p \to q) \land (q \to p) \\ \equiv (p \to q) \land (~ q \lor p) \end{array}$
and $p \lor q \to r \equiv\sim (p \lor q) \lor r$
$\begin{array}{l} \equiv (~ p \land ~ q) \lor r \\ \equiv (~ p \lor r) \land (~ q \lor r) \\ \equiv (p \to r) \land (q \to r) \end{array}$

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