Question

Considering truth table for $p\to \sim (p\wedge \sim q)$ as follows,
$\begin{array}{ccc}p& q& p\to \sim (p\wedge \sim q)\\ T& T& A\\ T& F& B\\ F& T& C\\ F& F& D\end{array}$
Identify the correct statement among the following

• A. The truth value of $A$ is opposite to that of $B$
• B. The truth value of $A$ is opposite to that of $C$
• C. The truth value of $A$ is opposite to that of $D$
• D. The truth value of $C$ is opposite to that of $D$

Answer 1

The correct option is A The truth value of $A$ is opposite to that of $B$

$\begin{array}{cccccc}p& q& \sim q& p\wedge \sim q& \sim (p\wedge \sim q)& p\to \sim (p\wedge \sim q)\\ T& T& F& F& T& T\\ T& F& T& T& F& F\\ F& T& F& F& T& T\\ F& F& T& F& T& T\end{array}$

The truth value of $A,C,D$ is true and that of $B$ is false. So clearly, the truth value of $A$ is opposite to that of $B$