Question

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

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

Answer 1

The correct option is B 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.