First slide

Introduction to mathematical reasoning

Question

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

Easy

A

tautology
B

contradiction
C

fallacy
D

none of these

Solution

$p \to (q \to r) \equiv\sim p \lor (q \to r)$
$\begin{array}{l} \equiv - p \lor (- q \lor r) \\ \equiv [(~ p) \lor (~ q)] \lor r \\ \equiv\sim (p \land q) \lor r \\ \equiv p \land q \to r \end{array}$
$∴$ given statement is a tautology.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App