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Question

Evaluate p~q~pq


A

A tautology

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B

A contradiction

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C

Both a tautology and a contradiction

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D

Neither a tautology nor a contradiction

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Solution

The correct option is B

A contradiction


Explanation for the correct option:

Finding the value :

We use the truth table method to find whether it is tautology or a contradiction.

Using associative laws and commutative laws,

p~q~pq=p~p~qq

where ~p is inverse of p

Similarly ~q is inverse of q

If pis Tand ~p is F then p~p is F

similarly if qis T and ~qis F then ~qq is F.

pq~p~qp~p~qqp~q~pq
TTFFFFF
TTFFFFF
FFTTFFF
FFTTFFF

Hence, (p~q)~pq is a contradiction as it has all false F.

Hence, option (B) is the correct answer.


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