Question

The logical statement $\left[\right(p\wedge q)\to p]\to (q\wedge \sim q)$ is

• A. neither a tautology nor a contradiction
• B. equivalent to $p\vee q$
• C. a tautology
• D. a contradiction

Answer 1

The correct option is D a contradiction

$\begin{array}{cccccccc}p& q& p\vee q& p\wedge q& (p\wedge q)\to p& \sim q& q\wedge \sim q& \left[\right(p\wedge q)\to p]\to [q\wedge \sim q]\\ T& T& T& T& T& F& F& F\\ T& F& T& F& T& T& F& F\\ F& T& T& F& T& F& F& F\\ F& F& F& F& T& T& F& F\end{array}$

The given compound statement is always false. So it is a contradiction.