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

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