First slide

Introduction to mathematical reasoning

Question

Statement $(p \land ~ q) \land (~ p \lor q)$ is

Moderate

A

a tautology
B

a contradiction
C

both a tautology and a contradiction
D

neither a tautology nor a contradiction

Solution

The truth table of $(p \land ~ q) \land (~ p \lor q)$ is as given below
The last column of the above truth table contains F only. So, the given statement is a contradiction.

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