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# The proposition $(p \Rightarrow \: ^{\sim}p) \wedge (^{\sim}p \Rightarrow p)$ is a

$\begin {array} {1 1} (A)\;tautology\: and\: contradiction & \quad (B)\;neither\: tautology\: nor \: contradiction \\ (C)\;contradiction & \quad (D)\;tautology \end {array}$

 p $^{\sim}p$ $p \Rightarrow \: ^{\sim}p$ $^{\sim}p \Rightarrow p$ $(p \Rightarrow \: ^{\sim}p) \wedge (^{\sim}p \: \Rightarrow p)$ T F F T F F T T F F
Ans : (C)
Thus the given proposition is a contradiction.

edited Jan 23, 2014