Which of the following sets is finite?

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(C) To determine which set is finite,we analyze each option:
$A$: The set of all prime numbers is infinite.
$B$: There are infinitely many quadrilat

Vedclass · Accepted Answer

$\{x \in \mathbb{N} \mid x^2 - 25 \le 0\}$

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(C) To determine which set is finite,we analyze each option:
$A$: The set of all prime numbers is infinite.
$B$: There are infinitely many quadrilaterals that can be drawn on a plane.
$C$: We are given the condition $x \in N$ (natural numbers) and $x^2 - 25 \leq 0$. Solving $x^2 \leq 25$ gives $-5 \leq x \leq 5$. Since $x \in N$,the possible values for $x$ are ${1, 2, 3, 4, 5}$. This set contains $5$ elements,so it is finite.
$D$: The set of multiples of $3$ in natural numbers is ${3, 6, 9, 12, \dots}$,which is infinite.
Therefore,the correct set is ${x: x \in N 	ext{ and } x^2 - 25 \leq 0}$.

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