(C) Step $1$: Analyze $S_1$. For $n=1$, $n^2+n+2 = 1+1+2 = 4$, which is divisible by $4$. Thus, $S_1$ is True.Step $2$: Analyze $S_2$. For $x=1$, $1-1

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(C) Step $1$: Analyze $S_1$. For $n=1$, $n^2+n+2 = 1+1+2 = 4$, which is divisible by $4$. Thus, $S_1$ is True.Step $2$: Analyze $S_2$. For $x=1$, $1-17 = -16 Step $3$: Analyze $S_3$. The equation $x^2+3x-10=0$ factors to $(x+5)(x-2)=0$, giving $x=-5$ or $x=2$. This is not true for all $n \in N$. Thus, $S_3$ is False.Step $4$: Analyze $S_4$. For all $n \in N$ (where $N = \{1, 2, 3, ...\}$), $n \geq 1$, so $n^2 \geq 1$. Thus, $S_4$ is True.Step $5$: Conclusion. Only $S_3$ is False.

Class 11 Mathematics Mathematical Reasoning Mathematical logic

Medium

Which of the following statements is/are False?
$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2: \exists x \in N$, such that $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \geq 1$.

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A
$S_1$ and $S_2$.
B
$S_1$ and $S_3$.
C
Only $S_3$.
D
$S_2$ and $S_4$.

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Which of the following statements is/are False?
$S_1 : \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2 : \exists x \in N$, such that $x - 17 < 20$.
$S_3 : \forall n \in N, n^2 + 3n - 10 = 0$.
$S_4 : \forall n \in N, n^2 \ge 1$.

MediumMHT CET 2026

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The minimum number of switches in the simplified form of the following switching circuit is

DifficultMHT CET 2026

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Which of the following sentences are statements? Give reasons for your answer.
The sum of all interior angles of a triangle is $180^{\circ}.$

Easy

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State the converse and contrapositive of the following statement:
$q:$ $I$ go to a beach whenever it is a sunny day.

Easy

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Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?

MediumJEE MAIN 2022

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Which of the following statements is/are False?$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.$S_2: \exists x \in N$, such that $x - 17 < 20$.$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.$S_4: \forall n \in N, n^2 \geq 1$.

Similar Questions

Which of the following statements is/are False?$S_1 : \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.$S_2 : \exists x \in N$, such that $x - 17 < 20$.$S_3 : \forall n \in N, n^2 + 3n - 10 = 0$.$S_4 : \forall n \in N, n^2 \ge 1$.

The minimum number of switches in the simplified form of the following switching circuit is

Which of the following sentences are statements? Give reasons for your answer.The sum of all interior angles of a triangle is $180^{\circ}.$

State the converse and contrapositive of the following statement:$q:$ $I$ go to a beach whenever it is a sunny day.

Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?

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Which of the following statements is/are False?
$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2: \exists x \in N$, such that $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \geq 1$.

Which of the following statements is/are False?
$S_1 : \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2 : \exists x \in N$, such that $x - 17 < 20$.
$S_3 : \forall n \in N, n^2 + 3n - 10 = 0$.
$S_4 : \forall n \in N, n^2 \ge 1$.

Which of the following sentences are statements? Give reasons for your answer.
The sum of all interior angles of a triangle is $180^{\circ}.$

State the converse and contrapositive of the following statement:
$q:$ $I$ go to a beach whenever it is a sunny day.