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. $\text{T,F,F}$
• B. $\text{F,T,T}$
• C. $\text{F,F,F}$
• D. $\text{T,T,F}$

Answer 1

The correct option is A $\text{T,F,F}$

$p\to (q\vee r):\text{False}$
$\therefore p:\text{True};q\vee r:\text{False}$
$p:\text{True};q:\text{False};r:\text{False}$

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 statement $p,q,r$ are $\text{T, F, F}$ respectively.