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# MCQs on Types of Set

{x: x is an integer neither positive nor negative} is ________ a) Empty set b) Non-empty set c) Finite set d) Non- empty and Finite set

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Answer: d

Explanation: Set = {0} non-empty and finite set.

{x: x is a real number between 1 and 2} is an ________

a) Infinite set

b) Finite set

c) Empty set

d) None of the mentioned

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Answer: a

Explanation: It is an infinite set as there are infinitely many real number between any two different real numbers.

Write set {1, 5, 15, 25,…} in set-builder form.

a) {x: either x=1 or x=5n, where n is a real number}

b) {x: either x=1 or x=5n, where n is a integer}

c) {x: either x=1 or x=5n, where n is an odd natural number}

d) {x: x=5n, where n is a natural number}

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Answer: c

Explanation: Set should include 1 or an odd multiple of 5.

. Express {x: x= n/ (n+1), n is a natural number less than 7} in roster form.

a) {1⁄2, 2⁄3, 4⁄5, 6⁄7}

b) {1⁄2, 2⁄3, 3⁄4, 4⁄5, 5⁄6, 6⁄7, 7⁄8}

c) {1⁄2, 2⁄3, 3⁄4, 4⁄5, 5⁄6, 6⁄7}

d) Infinite set

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Answer: c

Explanation: n/(n+1) = 1/(1+1) = 1⁄2 and n>7.

Number of power set of {a, b}, where a and b are distinct elements.

a) 3

b) 4

c) 2

d) 5

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Answer: b

Explanation: Power set of {a, b} = {∅, {a, b}, {a}, {b}}.

Which of the following is subset of set {1, 2, 3, 4}?

a) {1, 2}

b) {1, 2, 3}

c) {1}

d) All of the mentioned

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Answer: d

Explanation: There are total 16 subsets.

A = {∅,{∅},2,{2,∅},3}, which of the following is true?

a) {{∅,{∅}} ∈ A

b) {2} ∈ A

c) ∅ ⊂ A

d) 3 ⊂ A

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Answer: c

Explanation: Empty set is a subset of every set.

Subset of the set A= { } is?

a) A

b) {}

c) ∅

d) All of the mentioned

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Answer: d

Explanation: Every set is subset of itself and Empty set is subset of each set.

. {x: x ∈ N and x is prime} then it is ________

a) Infinite set

b) Finite set

c) Empty set

d) Not a set

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Answer: a

Explanation: There is no extreme prime, number of primes is infinite.

Convert set {x: x is a positive prime number which divides 72} in roster form.

a) {2, 3, 5}

b) {2, 3, 6}

c) {2, 3}

d) {∅}

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Answer: c

Explanation: 2 and 3 are the divisors of 72 which are prime.