Which of the following statements is true?

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(A) set is called finite if it has a finite number of elements. If a set $A$ is finite,then any subset $B$ of $A$ (where $B \subseteq A$) must also co

Vedclass · Accepted Answer

Every subset of a finite set is finite.

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(A) set is called finite if it has a finite number of elements. If a set $A$ is finite,then any subset $B$ of $A$ (where $B \subseteq A$) must also contain a finite number of elements,because the number of elements in $B$ cannot exceed the number of elements in $A$. Therefore,every subset of a finite set is finite. Option $B$ is false because a subset of an infinite set can be finite (e.g.,the set ${1}$ is a subset of the infinite set of natural numbers $\mathbb{N}$). Option $C$ is false because a subset of an infinite set can also be infinite (e.g.,the set of even numbers is a subset of $\mathbb{N}$). Option $D$ is false because a proper subset of a finite set always has fewer elements than the set itself,so it cannot be equivalent to the set.

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