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Mathematical Reasoning
hard
If the truth value of the statement $p \to \left( { \sim q \vee r} \right)$ is false $(F)$, then the truth values of the statement $p, q, r$ are respectively
A
$T, T, F$
B
$F, T, T$
C
$T, F, T$
D
$T, F, F$
(JEE MAIN-2019)
Solution
$P \to \left( { \sim q \vee r} \right)$
$ \sim p \vee \left( { \sim q \vee r} \right)$
$\left. \begin{array}{l}
\sim p \to F\\
\sim q \to F\\
\sim r \to F
\end{array} \right\} \Rightarrow \left. \begin{array}{l}
p \to T\\
q \to T\\
r \to F
\end{array} \right\}$
Standard 11
Mathematics
