Class 11 Mathematics Set Theory MCQs

Question : Given the sets
A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}.
Which of the following may be considered as universal set for all the three sets A, B and C?
(a) {0, 1, 2, 3, 4, 5, 6}
(b) f
(c) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(d) {1, 2, 3, 4, 5, 6, 7, 8}

Answer : C

Question : The set {x : x is an even prime number} can be written as
(a) {2}
(b) {2, 4}
(c) {2,14}
(d) {2, 4, 14}

Answer : A

Question : Let A and B be two non-empty subsets of a set
X such that A is not a subset of B, then :
(a) A is a subset of complement of B
(b) B is a subset of A
(c) A and B are disjoint
(d) A and the complement of B are nondisjoint.

Answer : D

Question : The set (A∪B∪C)∩(A∩B¢∩C¢)'∩C¢ is equal to
(a) B∩C¢
(b) A∩C
(c) B∩ C
(d) A∩C¢

Answer : A

Question : The set of intelligent students in a class is :
(a) A null set
(b) a singleton set
(c) a finite set
(d) Not a well defined collection

Answer : D

Question : Which of the following is correct for A – B?
(a) A ∩ B
(b) A' ∩ B
(c) A ∩ B'
(d) A' ∩ B'

Answer : C

Question : Which one is different from the others ?
(i) empty (ii) void (iii) zero (iv) null :
(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

Answer : D

Question : If A and B are two non-empty sets, then B ∩ (A ∪ B)c, where Xc denotes the complement of X, is equal to :
(a) Ac
(b) B
(c) A^c ∩ B
(d) f

Answer : D

Question : Which of the following collections are sets ?
(a) The collection of all the days of a week
(b) A collection of 11 best hockey player of India.
(c) The collection of all rich person of Delhi
(d) A collection of most dangerous animals of India.

Answer : A

Question : Which of the following properties are associative law ?
(a) A∪B = B∪ A
(b) A∪C = C ∪ A
(c) A∪D = D∪ A
(d) (A∪B)∪C = A∪(B∪C)

Answer : D

Question : If the sets A and B are as follows :
A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, then
(a) A – B = {1, 2}
(b) B – A = {5}
(c) [(A – B) – (B – A)] ∩ A = {1, 2}
(d) [(A – B) – (B – A)] ∪ A = {3, 4}

Answer : A

Question : If A = {1, 2, 3, 4, 5}, then the number of proper subsets of A is :
(a) 31
(b) 38
(c) 48
(d) 54

Answer : A

Question : The cardinality of the set P(P(P(f))) is
(a) 0
(b) 1
(c) 2
(d) 4
[P(A) represents power set of the set A]

Answer : D

Question : Let P be a set of squares, Q be set of parallelograms, R be a set of quadrilaterals and S be a set of rectangles. Consider the following :
1. P Ì Q
2. R Ì P
3. P Ì S
4. SÌ R
Which of the above are correct?
(a) 1, 2 and 3
(b) 1, 3 and 4
(c) 1, 2 and 4
(d) 3 and 4

Answer : B

Question : If A and B are finite sets, then which one of the following is the correct equation?
(a) n (A – B) = n (A) – n (B)
(b) n (A – B) = n (B – A)
(c) n (A – B) = n (A) – n (A ∩ B)
(d) n (A – B) = n (B) – n (A ∩ B)
[n (A) denotes the number of elements in A]

Answer : C

Question : If A = {x, y} then the power set of A is :
(a) {xx, yy}
(b) {f, x, y}
(c) {f,{x},{2y}}
(d) {f,{x},{y},{x,y}}

Answer : D

Question : Consider the following equations :
1. A – B = A – (A ∩ B)
2. A = (A ∩ B) ∪ (A – B)
3. A – (B ∪ C) = (A – B) ∪ (A – C)
Which of these is/are correct ?
(a) 1 and 3
(b) 2 only
(c) 2 and 3
(d) 1 and 2

Answer : D

Question : If A∪B ¹ f, then n(A∪B) = ?
(a) n(A) + n(B) - n(A∩B)
(b) n(A) - n(B) + n(A∩B)
(c) n(A) - n(B) - n(A∩ B)
(d) n(A) + n(B) + n(A∩ B)

Answer : A

Question : Let V = {a, e, i, o, u} and B = {a, i, k, u}. Value of V – B and B – V are respectively
(a) {e, 0} and {k}
(b) {e} and {k}
(c) {0} and {k}
(d) {e, 0} and {k, i}

Answer : A

Question : If A = {1, 2, 3, 4}, B = {2, 3, 5, 6} and C = {3, 4, 6,7}, then
(a) A – (B ∩ C) = {1, 3, 4}
(b) A – (B ∩ C) = {1, 2, 4}
(c) A – (B ∪ C) = {2, 3}
(d) A – (B ∪ C) = {f}

Answer : B

Question : If A and B are two sets, then A ∩ (A ∪ B)' equals :
(a) A
(b) B
(c) f
(d) None

Answer : C

Question : How many elements has P(A), if A = f ?
(a) two
(b) one
(c) three
(d) zero

Answer : B

Question : Let A = {a, b}, B = {a, b, c}. What is A∪B ?
(a) {a, b}
(b) {a, c}
(c) {a, b, c}
(d) {b, c}

Answer : C

Question : Which of the following is correct?
(a) A∪B¹A∪A'
(b) (A∩B)' = A'∪B'
(c) (A' ∪B') ¹A'∪A
(d) (A∩B)' = A'∩B'

Answer : D

Question : What is the simplified representation of
(A´ ∩ B´∩C) ∪ (B∩C) ∪ (A ∩ C), where A,B, C are subsets of a set X?
(a) A
(b) B
(c) C
(d) X∩ ( A∪ B∪ C)

Answer : C

Question : What does the shaded portion of the Venn diagram given above represent?
(a) (P∩Q)∩(P∩R)
(b) ((P∩Q) - R)∪((P∩R) -Q)
(c) ((P∪Q) -R)∩((P∩R) -Q)
(d) ((P∩Q)∪R)∩((P∪Q) -R)

Answer : B 

Question : If the sets A and B are given by A = {1, 2, 3, 4},
B = {2, 4, 6, 8, 10} and the universal set
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then
(a) (A∪B)'= {5, 7, 9}
(b) (A∩B)'= {1, 3, 5, 6, 7}
(c) (A∩B)' = {1, 3, 5, 6, 7, 8}
(d) None of these

Answer : A

Question : If A and B are finite sets then (A – B) ∪ (B – A) equals:
(a) (A ∪ B) – A
(b) (A – B) ∪ B
(c) (A ∪ B) – (A ∩ B)
(d) (A – B) ∪ A

Answer : C

Question : Let A, B, C be any three non-empty sets. If A∪B = A ∪C, then which one of the following is definitely true?
(a) B = C
(b) B⊆C
(c) C⊆B
(d) none of these

Answer : D