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Question

Which of the following is logically equivalent to ~~pq?


A

pq

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B

p~q

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C

~pq

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D

~p~q

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Solution

The correct option is D

~p~q


Truth table of pq

pqpq
TTT
TFF
FTT
FFT

Truth table of ~p

p~p
TF
FT

Truth table of pq.

pqpq
TTT
TFF
FTF
FFF

Given logical statement is ~~pq.

The truth table of the given statement is:

pq~p~pq~~pq
TTFTF
TFFTF
FTTTF
FFTFT

The explanation for the correct option:

The truth table of the correct option is:

pq~p~q~p~q
TTFFF
TFFTF
FTTFF
FFTTT

The outputs of ~p~q are the same as the outputs of ~~pq.

Hence, the correct option is D)~p~q.

The explanation for the incorrect options:

The truth table of the incorrect options is:

pq~p~qpqp~q~pq
TTFFTFF
TFFTFTF
FTTFFFT
FFTTFFF

The outputs of the other three options are not the same as the outputs of ~~pq.

Hence, the incorrect options are A),B) and C).


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