Question

If $p\to (q\vee r)$ is false, then the truth values of $p,q,r$ are respectively (where $T$ is true and $F$ is false)

• A. $T,F,F$
• B. $F,T,T$
• C. $F,F,F$
• D. $T,T,F$

Answer 1

The correct option is A $T,F,F$

$p\to (q\vee r)$ is false.
$\therefore p$ is true; $q\vee r$ is false.
$\Rightarrow p$ is true; $q$ is false; $r$ is false.

Alternate Solution :
$\begin{array}{ccccc}p& q& r& q\vee r& p\to q\vee r\\ T& T& T& T& T\\ T& T& F& T& T\\ T& F& T& T& T\\ T& F& F& F& F\\ F& T& T& T& T\\ F& T& F& T& T\\ F& F& T& T& T\\ F& F& F& F& T\end{array}$

Clearly, from truth table, $p\to (q\vee r)$ is false when truth values of statements $p,q,r$ are $T,F,F$ respectively.