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Question

Which of the following statements is a tautology?


A

~qpq

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B

~qpp~p

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C

~qpp~p

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D

pq~pq

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Solution

The correct option is C

~qpp~p


Explanation for the correct option:

A tautology is a compound statement in Maths that always results in a Truth value.

It doesn’t matter what the individual part consists of, the result in tautology is always true.

The possible truth table is:

pq~p~q~qpp~p~qpp~p
TTFFFTT
TFFTTTT
FTTFFTT
FFTTFTT

All outputs of ~qpp~p are true.

Hence, the correct option is C)~qpp~p

Explanation for the incorrect options:

The possible truth table is:

pq~p~q~qppqp~p~pq~qpq~qpp~ppq~pq
TTFFFTFFFFF
TFFTTFFTFFF
FTTFFFFTFFF
FFTTFFFTFFF

The outputs of the options A),B),D) are not a tautology.

Hence, these options are incorrect.

Hence option (C) is the correct option.


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