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Mathematical Reasoning
hard
Let $p , q , r$ be three statements such that the truth value of $( p \wedge q ) \rightarrow(\sim q \vee r )$ is $F$. Then the truth values of $p , q , r$ are respectively
A
$ T , F , T$
B
$F , T , F$
C
$T , T , F$
D
$T , T , T$
(JEE MAIN-2020)
Solution
$(p \wedge q) \rightarrow(\sim q \vee r)=f a l s e$
when $( p \wedge q )= T$
and $\quad(\sim q \vee r)=F$
So $\quad( p \wedge q )= T$ is possible when $p = q =$ true
$\therefore \quad \sim q =$ False $( q =$ true $)$
So $(\sim q \vee r )=$ False is possible if $r$ is false
$\therefore p = T , q = T , r = F$
Standard 11
Mathematics
