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The false statement in the following is...

The false statement in the following is

A

` p ^^ ( ~ p)` is a contradiction

B

` ( p to q) harr ( ~ q to ~ p)` is a contradiction

C

` ~ ( ~ p) harr` is a tautology

D

` P vv (~ p)` is a tautology

Text Solution

Verified by Experts

The correct Answer is:
B
The last column in the turth table of ` P ^^ ( ~ p) ` consists of F only , So, ` p ^^ ~ p` is a contradition and hence it is not a false statement.
We observe that the last column in the truth table of ` ( p to q) harr ( ~ q to ~ p)` constains T only. So, it is a tautology not a contradiction.
clearly,` ~ ( ~ p) cong p . " So " , ~ ( ~ p ) harr p `is a tautology.
the last column in the truth table for ` p vv (~ p)` contains T only , So, it is a tautology.
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