76. The range of the relation R = (1, 2), (2, 4), (3, 6) is:
- 2, 4, 6
- 4, 6
- 1, 2, 3
- 1, 2, 3, 4, 6
Answer: A) 2, 4, 6
Explanation: The range is the set of second elements of the ordered pairs. SLO M-09-A-15 · Knowledge
MCQs / Mathematics / Sets and Functions
Sets and Functions MCQs — Mathematics (page 4)
155 multiple-choice questions on Sets and Functions from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.
77. Verify the distributive law of intersection over union: with A = 3, 4, 6, 7, 9, B = 4, 5, 8, 9, C = 3, 4, 5, 8, both A cap (B cup C) and (A cap B) cup (A cap C) equal:
- 4
- 3, 4, 5, 8
- 3, 4, 5, 6, 7, 8, 9
- 3, 4, 9
Answer: D) 3, 4, 9
Explanation: Working out each side separately gives the same set 3, 4, 9, which verifies A cap (B cup C) = (A cap B) cup (A cap C). SLO M-09-A-13 · Application
78. A taxi charges Rs. 150 plus Rs. 40 per km. Which ordered pair (km, fare) belongs to this relation?
- (5, 390)
- (5, 350)
- (5, 200)
- (350, 5)
Answer: B) (5, 350)
Explanation: Fare = 150 + 40 5 = 350, written as (km, fare). SLO M-09-A-16 · Application
79. In a Venn diagram, the rectangle stands for:
- the intersection
- the complement of A
- the universal set
- the empty set
Answer: C) the universal set
Explanation: The universal set U is drawn as a rectangle; other sets are circles inside it. SLO M-09-A-12 · Understanding
80. The relation y = x^2 on the domain -2, -1, 0, 1 written as ordered pairs is:
- (-2, 5), (-1, 2), (0, 1), (1, 2)
- (-2, 4), (-1, 1), (0, 0), (1, 1)
- (-2, -2), (-1, -1), (0, 0), (1, 1)
- (4, -2), (1, -1), (0, 0), (1, 1)
Answer: B) (-2, 4), (-1, 1), (0, 0), (1, 1)
Explanation: Substitute each x: (-2, 4), (-1, 1), (0, 0), (1, 1). SLO M-09-A-16 · Application
81. The table shows a relation. x 1 2 3 4 --------------- y 3 5 7 9 As a set of ordered pairs it is:
- (1, 3), (2, 5)
- 1, 2, 3, 3, 4, 5, 7, 9
- (1, 3), (2, 5), (3, 7), (4, 9)
- (3, 1), (5, 2), (7, 3), (9, 4)
Answer: C) (1, 3), (2, 5), (3, 7), (4, 9)
Explanation: Pair each x with the y below it. SLO M-09-A-16 · Application
82. In a survey of 44 shoppers at a mall, 27 bought clothes, 18 bought shoes and 9 bought both. How many shoppers are in at least one of the two groups?
- 36
- 27
- 18
- 8
Answer: A) 36
Explanation: At least one = 27 + 18 - 9 = 36; first group only = 18; second group only = 9; exactly one = 27; neither = 44 - 36 = 8. So the answer is 36. SLO M-09-A-14 · Application
83. n(A) = 60, n(B) = 45 and n(A cap B) = 20. Find n(A cup B).
- 105
- 40
- 125
- 85
Answer: D) 85
Explanation: n(A cup B) = n(A) + n(B) - n(A cap B) = 60 + 45 - 20 = 85. SLO M-09-A-12 · Understanding
84. If A = 1, 2, 7, 8, 10, B = 1, 7, 10, 11, 12 and C = 2, 10, 11, 12, find A cup B cup C.
- 1, 2, 7, 8, 10, 11, 12
- 1, 2, 7, 10
- 1, 7
- 11, 12
Answer: A) 1, 2, 7, 8, 10, 11, 12
Explanation: Work out the brackets first. A cup B cup C = 1, 2, 7, 8, 10, 11, 12. SLO M-09-A-11 · Application
85. Which set is always equal to (A cap B)'?
- A' cup B'
- A' cap B'
- A cup B
- A cap B'
Answer: A) A' cup B'
Explanation: (A cap B)' = A' cup B' — the De Morgan's law. SLO M-09-A-13 · Application
86. If n(A) = 1 and n(B) = 3, how many binary relations are there from A to B?
- 7
- 8
- 3
- 16
Answer: B) 8
Explanation: A relation is any subset of A B, which has 3 elements, so there are 2^3 = 8 relations. SLO M-09-A-15 · Knowledge
87. Which formula gives the nth term of 7, 11, 15, 19, ldots?
- 7n+4
- 4n+4
- 4n+7
- 4n+3
Answer: D) 4n+3
Explanation: The terms go up by 4, so the rule is 4n + c. With n = 1: 4 + c = 7, so c = 3 and the rule is 4n+3. SLO M-09-A-10 · Understanding
88. The inverse of the relation (1, 4), (2, 5), (3, 6) is:
- (4, 5), (5, 6)
- (4, 1), (5, 2), (6, 3)
- (-1, -4), (-2, -5), (-3, -6)
- (1, 4), (2, 5), (3, 6)
Answer: B) (4, 1), (5, 2), (6, 3)
Explanation: Swap the elements of each ordered pair. SLO M-09-A-16 · Application
89. If n(A) = 2 and n(B) = 2, how many binary relations are there from A to B?
- 17
- 16
- 4
- 15
Answer: B) 16
Explanation: A relation is any subset of A B, which has 4 elements, so there are 2^4 = 16 relations. SLO M-09-A-15 · Knowledge
90. If A = 0, 1 and B = 1, 2, then A B =
- (0, 1), (0, 2), (1, 1), (1, 2)
- (0, 1), (1, 2)
- 0, 1, 1, 2
- (1, 0), (1, 1), (2, 0), (2, 1)
Answer: A) (0, 1), (0, 2), (1, 1), (1, 2)
Explanation: A B is the set of all ordered pairs (a, b) with a in A, b in B: (0, 1), (0, 2), (1, 1), (1, 2). SLO M-09-A-15 · Knowledge
91. The statement A cup (B cup C) = (A cup B) cup C is the:
- associative law of union
- De Morgan's law
- distributive law of intersection over union
- distributive law of union over intersection
Answer: A) associative law of union
Explanation: It is the associative law of union. SLO M-09-A-13 · Application
92. Verify the De Morgan's law: with U = 1, 2, ldots, 10, A = 2, 5, 6, 7, 10, B = 3, 4, 5, 8, C = 3, 8, 9, 10, both (A cap B)' and A' cup B' equal:
- 1, 2, 3, 4, 6, 7, 8, 9, 10
- 2, 3, 4, 5, 6, 7, 8, 9, 10
- 3, 8, 10
- varnothing
Answer: A) 1, 2, 3, 4, 6, 7, 8, 9, 10
Explanation: Working out each side separately gives the same set 1, 2, 3, 4, 6, 7, 8, 9, 10, which verifies (A cap B)' = A' cup B'. SLO M-09-A-13 · Application
93. n(A) = 40, n(B) = 35, n(C) = 28, n(A cap B) = 12, n(B cap C) = 9, n(A cap C) = 10 and n(A cap B cap C) = 5. Find n(A cup B cup C).
- 67
- 77
- 103
- 72
Answer: B) 77
Explanation: n(A cup B cup C) = 40 + 35 + 28 - 12 - 9 - 10 + 5 = 77. SLO M-09-A-12 · Understanding
94. The point (2, 7) lies in quadrant:
- IV
- II
- I
- III
Answer: C) I
Explanation: Quadrant I: (+, +); II: (-, +); III: (-, -); IV: (+, -). SLO M-09-A-16 · Application
95. 1 + 2 + 3 + s + 50 =
- 1300
- 1250
- 2550
- 1275
Answer: D) 1275
Explanation: Pair the numbers (1 + 50, 2 + 49, …): 25 51 = 1275, i.e. 50 512. SLO M-09-A-10 · Understanding
96. If A = 3, 5, 6, 9, 10, B = 2, 4, 7, 9, 12 and C = 3, 4, 8, 11, find (A cap B) - C.
- varnothing
- 9
- 2, 3, 4, 7, 8, 11, 12
- 3, 4
Answer: B) 9
Explanation: Work out the brackets first. (A cap B) - C = 9. SLO M-09-A-11 · Application
97. The domain of the relation R = (-1, 1), (0, 0), (1, 1), (2, 4) is:
- 0, 1, 4
- -1, 0, 0, 1, 1, 2, 4
- -1, 0, 1, 2
- -1, 0, 1
Answer: C) -1, 0, 1, 2
Explanation: The domain is the set of first elements of the ordered pairs. SLO M-09-A-15 · Knowledge
98. In a Venn diagram of A, B, C inside U, the region inside C but outside A and B is:
- (A cup B) - C
- C - A
- C cap A cap B
- C - (A cup B)
Answer: D) C - (A cup B)
Explanation: The region inside C but outside A and B is C - (A cup B). SLO M-09-A-12 · Understanding
99. Verify the distributive law of union over intersection: with A = 1, 2, 4, 6, 10, B = 1, 7, 8, 10, C = 1, 2, 4, 7, both A cup (B cap C) and (A cup B) cap (A cup C) equal:
- 1
- 1, 2, 4, 7
- 1, 2, 4, 6, 7, 10
- 1, 2, 4, 6, 7, 8, 10
Answer: C) 1, 2, 4, 6, 7, 10
Explanation: Working out each side separately gives the same set 1, 2, 4, 6, 7, 10, which verifies A cup (B cap C) = (A cup B) cap (A cup C). SLO M-09-A-13 · Application
100. Which set is always equal to A cup (B cap C)?
- (A cup B) cap C
- (A cap B) cup (A cap C)
- A cup B cup C
- (A cup B) cap (A cup C)
Answer: D) (A cup B) cap (A cup C)
Explanation: A cup (B cap C) = (A cup B) cap (A cup C) — the distributive law of union over intersection. SLO M-09-A-13 · Application
Practise Sets and Functions MCQs