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Finite and Infinite Set

Which of the ...

Question

Which of the following is a finite set ?

A

A = {x : x \in N and x is a prime number}

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B

B = {x : x is a real number between 1 and 10}

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C

C = {x : x is a perfect square number between 0 and 99}

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D

D = {x : x is an integer less than 20}

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Solution

The correct option is C $C = {x : x is a perfect square number between 0 and 99}$
$A = {x : x \in N and x is a prime number}$
There are infinite prime numbers.
$\Rightarrow A$ is not a finite set.

$B = {x : x is a real number between 1 and 10}$
There are infinite real numbers between $1$ and $10.$
$\Rightarrow B$ is not a finite set.

$C = {x : x is a perfect square number between 0 and 99}$
$C = {1, 4, 9, 16, 25, 36, 49, 64, 81}$
$\Rightarrow C$ is a finite set.

$D = {x : x is an integer less than 20}$
There are infinite integers below $20.$
$\Rightarrow D$ is not a finite set.

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Finite and Infinite Set

Standard XII Mathematics

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