First slide

Introduction to mathematical reasoning

Question

The statement $[p \land (p \to q)] \to q$ , is

Easy

A

a fallacy
B

a tautology
C

neither a fallacy nor a tautology
D

not a compound statement

Solution

$\begin{array}{l} p \land (p \to q) \to q \\ \equiv [p \land (~ p \lor q)] \to q \\ \equiv [(p \land (~ p)) \lor (p \land q)] \to q \\ \equiv [F \lor (p \land q)] \to q \\ \equiv (p \land q) \to q \\ \equiv ~ (p \land q) \lor q \\ \equiv (~ p \lor ~ q) \lor q \\ \equiv ~ p \lor (~ q \lor q) \\ \equiv (~ p) \lor T \equiv T \end{array}$

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