JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Question Bank Self Evaluation Test - Mathematical Reasoning

The propositions \[(p\Rightarrow \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\] is a

A) Tautology and contradiction

B) Neither tautology nor contradiction

C) Contradiction

D) Tautology

Correct Answer: C

Solution :

[c]

\[p\]	\[\tilde{\ }q\]	\[p\Rightarrow \tilde{\ }p\]	\[\tilde{\ }p\Rightarrow p\]	\[(p\Rightarrow \tilde{\ }p)\]\[\wedge (\tilde{\ }p\Rightarrow p)\]
T	F	F	T	F
F	T	T	F	F

Clearly, \[(p\Rightarrow \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\] is a contradiction.