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Mathematical Reasoning
hard
Let $p$ and $q$ be any two logical statements and $r:p \to \left( { \sim p \vee q} \right)$. If $r$ has a truth value $F$, then the truth values of $p$ and $q$ are respectively
A
$F,F$
B
$T,T$
C
$T,F$
D
$F,T$
(JEE MAIN-2013)
Solution
$p \to \left( { \sim p \vee q} \right)$ has truth value $F$.
It means $p \to \left( { \sim p \vee q} \right)$ is false.
It means $p$ is true and ${ \sim p \vee q}$ is false.
$ \Rightarrow $ $p$ is true and both ${ \sim p}$ and $q$ are false.
$ \Rightarrow $$p$ is true and $q$ is false.
Standard 11
Mathematics
