Question

If $p,q,r$ have truth values $T,F,T$ respectively, then which among the following will have truth value as TRUE.

• A. $(p\to q)\wedge r$
• B. $(p\to q)\vee q$
• C. $(p\wedge q)\wedge (p\vee r)$
• D. $q\to (p\wedge r)$

Answer 1

The correct option is D $q\to (p\wedge r)$

$\begin{array}{ccccccccccc}p& q& r& p\to q& p\wedge q& p\wedge r& p\vee r& (p\to q)\wedge r& (p\to q)\vee q& (p\wedge q)\wedge (p\vee r)& q\to (p\wedge r)\\ T& F& T& F& F& T& T& F& F& F& T\end{array}$

From the above table, it is clear that $q\to (p\wedge r)$ is TRUE.