(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

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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

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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Show that the statement $p:$ 'If $x$ is a real number such that $x^{3}+4x=0$,then $x$ is $0$' is true by the method of contrapositive.

Medium

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For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
To enter a country,you need a passport or a voter registration card.

Easy

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By giving a counterexample,show that the following statement is not true.
$q:$ The equation $x^{2}-1=0$ does not have a root lying between $0$ and $2$.

Medium

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Which of the following statement patterns is a contradiction?

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If $p: \forall n \in N, n^2+n$ is an even number and $q: \forall n \in N, n^2-n$ is an odd number,then the truth values of $p \wedge q, p \vee q$ and $p \rightarrow q$ are respectively:

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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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Show that the statement $p:$ 'If $x$ is a real number such that $x^{3}+4x=0$,then $x$ is $0$' is true by the method of contrapositive.

For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.To enter a country,you need a passport or a voter registration card.

By giving a counterexample,show that the following statement is not true.$q:$ The equation $x^{2}-1=0$ does not have a root lying between $0$ and $2$.

Which of the following statement patterns is a contradiction?

If $p: \forall n \in N, n^2+n$ is an even number and $q: \forall n \in N, n^2-n$ is an odd number,then the truth values of $p \wedge q, p \vee q$ and $p \rightarrow q$ are respectively:

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For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
To enter a country,you need a passport or a voter registration card.

By giving a counterexample,show that the following statement is not true.
$q:$ The equation $x^{2}-1=0$ does not have a root lying between $0$ and $2$.