(A) The implication $p \to (\sim q \vee r)$ is false $(F)$ only when the antecedent is true $(T)$ and the consequent is false $(F)$.$1$. $p = T$$2$. $

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(A) The implication $p \to (\sim q \vee r)$ is false $(F)$ only when the antecedent is true $(T)$ and the consequent is false $(F)$.$1$. $p = T$$2$. $(\sim q \vee r) = F$For the disjunction $(\sim q \vee r)$ to be false,both components must be false:$\sim q = F \implies q = T$$r = F$Therefore,the truth values are $p = T, q = T, r = F$.

Class 11 Mathematics Mathematical Reasoning Mathematical logic

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If the truth value of the statement $p \to (\sim q \vee r)$ is false $(F)$,then the truth values of the statements $p, q, r$ are respectively:

JEE MAIN 2019 All JEE MAIN

A
$T, T, F$
B
$F, T, T$
C
$T, F, T$
D
$T, F, F$

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Mathematical Reasoning

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DifficultJEE MAIN 2013

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If the truth value of the statement $p \to (\sim q \vee r)$ is false $(F)$,then the truth values of the statements $p, q, r$ are respectively:

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If the statement $p \leftrightarrow (q \rightarrow p)$ is false,then the true statement/statement pattern is

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Statement $-1$: The statement $A \to (B \to A)$ is equivalent to $A \to (A \vee B)$.
Statement $-2$: The statement $\sim [(A \wedge B) \to (\sim A \vee B)]$ is a tautology.