Q63 / 120 · VITEEE 2014 · Mathematics
The statement $(\mathrm{p} \Rightarrow \mathrm{q}) \Leftrightarrow(\sim p \wedge q)$ is a
- Atautology
- Bcontradiction
- Correct answerCNeither (a) nor (b)
- DNone of these
Solution
\begin{array}{c|c|c|c|c|c}
\hline \mathrm{p} & \mathbf{q} & \mathbf{p} & \mathbf{p} \Rightarrow \mathbf{q} & \sim \mathbf{p}^{\wedge} \mathbf{q} & (\mathbf{p} \Rightarrow \mathbf{q}) \Leftrightarrow\left(\sim \mathbf{p}^{\wedge} \mathbf{q}\right) \\
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\
\hline
\end{array}
Hence, given statement is neither tautology nor contradiction.
Hence, the correct answer is option: 'C'.