If truth value of statement p to left( { ∼ q vee r} right) is false (F) , then truth v

English

Gujarati

Hindi

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

$T, T, F$

$F, T, T$

$T, F, T$

$T, F, F$

(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

The conditional $(p \wedge q) ==> p$ is

medium

If the Boolean expression $( p \wedge q ) \circledast( p \otimes q )$ is a tautology, then $\circledast$ and $\otimes$ are respectively given by

medium

(JEE MAIN-2021)

If $\mathrm{p} \rightarrow(\mathrm{p} \wedge-\mathrm{q})$ is false, then the truth values of $p$ and $q$ are respectively

hard

(JEE MAIN-2020)

Which of the following statements is $NOT$ logically equivalent to $\left( {p \to \sim p} \right) \to \left( {p \to q} \right)$?

normal

The negation of the statement $''96$ is divisible by $2$ and $3''$ is