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Question

Which of the following is not true for any two statements p and q?


A

~p~q~pq

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B

~(pq)=(~p)(~q)

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C

q~q is contradiction

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D

~[p(~p)] is a tautology

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Solution

The correct option is B

~(pq)=(~p)(~q)


Explanation for correct option

A tautology is a compound statement that is always true.

Signs of tautology:

Symbol Meaning
~Not
And
Or
Implies or If-then

Make truth table to check the relation~pq=~p~q

p~pq~qpq~pq~p~q
TFTFTFF
TFFTTFT
FTTFTFT
FTFTFTT

From the table it clear that ~pq~p~qis is

Explanation for incorrect option

Option (A)

Make truth table to check the relation ~p~q~pq

p~pq~qp~q~p~q~pq
TFTFTFF
TFFTTFF
FTTFFTT
FTFTTFF

Thus the relation~p~q~pq is true.

Option (C)

q~qq~q
TFF
FTF

Since the results are false. So it is a contradiction.

For option (D)

p~pp~p~p~p
TFFT
FTFT

Since the results are true. So ~p~p is a tautology

Hence option (B) is the correct option.


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