(B) $1$. An implication $A \to B$ is false only when $A$ is true and $B$ is false.$2$. Here, $A = (p \wedge q)$ and $B = (r \vee \sim s)$.$3$. For $(p

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(B) $1$. An implication $A \to B$ is false only when $A$ is true and $B$ is false.$2$. Here, $A = (p \wedge q)$ and $B = (r \vee \sim s)$.$3$. For $(p \wedge q)$ to be true, both $p$ and $q$ must be true $(T)$.$4$. For $(r \vee \sim s)$ to be false, both $r$ and $\sim s$ must be false $(F)$.$5$. If $r$ is false $(F)$ and $\sim s$ is false $(F)$, then $s$ must be true $(T)$.$6$. Thus, the truth values are $p=T, q=T, r=F, s=T$.

Class 11 Mathematics Mathematical Reasoning Mathematical logic

Medium

The statement pattern $(p \wedge q) \to (r \vee \sim s)$ is false. Then the truth values of $p, q, r$ and $s$ are respectively

MHT CET 2026 All MHT CET

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

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Class 11

Mathematics Questions

Chapter

Mathematical Reasoning

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Mathematical logic

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The statement pattern $(p \wedge q) \to (r \vee \sim s)$ is false. Then the truth values of $p, q, r$ and $s$ are respectively

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Which of the following is the negation of the statement "For all $M > 0$,there exists $x \in S$ such that $x \geqslant M$"?

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