Set Theory Multiple Choice Questions and Answers

(1) A __________ is an ordered collection of objects.

[A] Relation

[B] Function

[C] Set

[D] Proposition

Answer: Set

(2) Power set of empty set has exactly _________ subset.

[A] One

[B] Two

[C] Zero

[D] Three

Answer: One

(3) What is the Cartesian product of A = {1, 2} and B = {a, b}?

[A] {(1, a), (1, b), (2, a), (b, b)}

[B] {(1, 1), (2, 2), (a, a), (b, b)}

[C] {(1, a), (2, a), (1, b), (2, b)}

[D] {(1, 1), (a, a), (2, a), (1, b)}

Answer: {(1, a), (2, a), (1, b), (2, b)}

(4) Which of the following two sets are equal?

[A] A = {1, 2} and B = {1}

[B] A = {1, 2} and B = {1, 2, 3}

[C] A = {1, 2, 3} and B = {2, 1, 3}

[D] A = {1, 2, 4} and B = {1, 2, 3}

Answer: A = {1, 2, 3} and B = {2, 1, 3}

(5) The members of the set S = {x | x is the square of an integer and x < 100} is ________________

[A] {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}

[B] {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

[C] {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}

[D] {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

Answer: {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

(6) The number of subsets of a set containing n elements is

[A] n

[B] 2n 1

[C] n2

[D] 2n

Answer: 2n

(7) If A = {1, 3, 5, B} and B = {2, 4} then

[A] 4  A

[B] {4}  A

[C] B  A

[D] 180° and 0°

Answer: None of these

(8) The symmetric difference of A = {1, 2, 3} and B = {3, 4, 5} is

[A] {1, 2}

[B] {1, 2, 4, 5}

[C] {4, 3}

[D] {2, 5, 1, 4, 3}

Answer: {1, 2, 4, 5}

(9) If A = {1, 2} and B = {0, 1}, then A  B is

[A] {(1, 0) (1, 1), (2, 0) (2, 1)}

[B] {(1, 0), (2, 1)}

[C] {(1, 1), (1, 2), (0, 1) (0, 2)

[D] None of these

Answer: {(1, 0) (1, 1), (2, 0) (2, 1)}

(10) If A = {1, 2, 3}, B = {3, 4, 5}, then (A  B)  A is

[A] {(1, 3), (2, 3), (3, 3)}

[B] {(3, 1), (3, 2), (3, 3)

[C] {(1, 3), (3, 1), (3, 2)

[D] None of these

Answer: {(3, 1), (3, 2), (3, 3)

(11) If A = {2, 3, 4}, B = {2, 5, 6}, then (A  B)  (A  B) is

[A] {(3, 2), (3, 3), (3, 5)

[B] {(3, 2), (3, 5) (3, 6)

[C] {(3, 2), (3, 5)}

[D] None of these

Answer: {(3, 2), (3, 5)}

(12) If A = {1, 2}, B = {2, 3} and C = {4}, then A  B  C is

[A] {(1, 2, 4), (2, 2, 4), (1, 3, 4), (2, 3, 4)

[B] {(1, 2, 4), (1, 4, 3), (2, 3, 4)

[C] {(1, 3, 4), (2, 3, 4), (2, 1, 3), (2, 2, 4)

[D] None of these

Answer: {(1, 2, 4), (2, 2, 4), (1, 3, 4), (2, 3, 4)

(13) If A = {2, 3} and B = {x | x  N and x < 3}, then A  B is

[A] {(2, 1), (2, 2), (3, 1), (3, 2)}

[B] {(1, 2), (1, 3), (2, 2), (2, 3)}

[C] {(1, 2), (2, 2), (3, 3), (3, 2)

[D] None of these

Answer: {(2, 1), (2, 2), (3, 1), (3, 2)}

(14) If R = {x, y) : x, y  Z, x2 + y2  4} is a relation in z, then domain of R is

[A] {0, 1, 2}

[B] {– 2, – 1, 0}

[C] {– 2, – 1, 0, 1, 2}

[D] None of these

Answer: {– 2, – 1, 0, 1, 2}

(15) R is a relation defined in Z by aRb if and only if ab  0, then R is

[A] reflexive

[B] symmetric

[C] transitive

[D] equivalence

Answer: equivalence

(16) If R be relation ‘<‘ from A = {1, 2, 3, 4} to B = {1, 3, 5} ie, (a, b)  R iff a < b, then RoR– 1 is

[A] {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

[B] {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}

[C] {(3, 3), (3, 5), (5, 3), (5, 5)}

[D] { (3, 3), (3, 4), (4, 5)}

Answer: {(3, 3), (3, 5), (5, 3), (5, 5)}

(17) R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R – 1 is

[A] {(11, 8), (13, 10)}

[B] {(8, 11), (10, 13)}

[C] {(8, 11), (9, 12), (10, 13)}

[D] None of the above

Answer: {(8, 11), (10, 13)}

(18) Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then, n (X Y) is equal to

[A] 4

[B] 6

[C] 8

[D] 12

Answer: 12

(19) Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is

[A] 7

[B] 9

[C] 10

[D] 12

Answer: 7

(20) The relation R defined on the set of natural numbers as {(a, b): a differs from b by 3} is given

[A] {(1, 4), (2, 5), (3, 6), ….}

[B] { (4, 1), (5, 2), (6, 3), ….}

[C] {(4, 1), (5, 2), (6, 3), ….}

[D] None of the above

Answer: { (4, 1), (5, 2), (6, 3), ….}

Set Theory MCQs | Set Theory Multiple Choice Questions and Answers

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