Which of the following statements is/are Fals | vedclass

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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 $x=1$, $1-1

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Only $S_3$.

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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.

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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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 $x - 17 < 20$.$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.$S_4: \forall n \in N, n^2 \geq 1$.