Set Theory MCQs | Set Theory Multiple Choice Questions and Answers

Sports GK Questions and Answers 2024 (Latest Updated)

Awards & Honours GK Questions 2024 (Latest Updated)

Questions
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
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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), ….}
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