Question

3. Which of the following sets is a finite set?
(A) { x:x is an integer and x2 > 0)
(B) A = { x:x is a prime number greater then 10)
(C) (x:x is an integer and x2=x?
(D) A = {x:x is an integer less than 20%​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the following sets is a finite set

(A) { x:x is an integer and x² > 0}

(B) A = { x:x is a prime number greater then 10}

(C) { x:x is an integer and x² = x}

(D) A = { x:x is an integer less than 20%}

CONCEPT TO BE IMPLEMENTED

SET

A Set is a well defined collection of distinct objects

Finite Set

A set is said to be finite set if it contains finite number of elements

EVALUATION

CHECKING FOR OPTION : A

Here the given set is

{ x:x is an integer and x² > 0}

Since there infinite number integer value of x such that x² > 0

So the above set is infinite set

CHECKING FOR OPTION : B

Here the given set is

{ x:x is a prime number greater than 10}

Since there infinite number prime number greater than 10

So the above set is infinite set

CHECKING FOR OPTION : C

Here the given set is

{ x:x is an integer and x² = x }

x² = x gives x = 0 , 1

So { x:x is an integer and x² = x } = {0,1}

Since there finite number integer value of x such that x² = x

So the above set is finite set

CHECKING FOR OPTION : D

Here the given set is

{ x:x is an integer less than 20% }

Since there infinite number integer value of x such that x is less than 20%

So the above set is infinite set

FINAL ANSWER

Hence the correct option is

(C) { x:x is an integer and x² = x}

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