(D) The implication $(p \wedge q) \rightarrow (\sim q \vee r)$ is false $(F)$ only when the antecedent $(p \wedge q)$ is true $(T)$ and the consequent

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(D) The implication $(p \wedge q) \rightarrow (\sim q \vee r)$ is false $(F)$ only when the antecedent $(p \wedge q)$ is true $(T)$ and the consequent $(\sim q \vee r)$ is false $(F)$.For $(p \wedge q)$ to be true,both $p$ and $q$ must be true $(T)$.For $(\sim q \vee r)$ to be false,both $\sim q$ and $r$ must be false $(F)$.Since $q$ is true,$\sim q$ is false. For $r$ to be false,$r$ must be $F$.Thus,the truth values are $p = T, q = T, r = F$.

Class 11 Mathematics Mathematical Reasoning Mathematical logic

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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:

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

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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:

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