SETS AND RELATIONS

1

Bilal defines a relation R = {(x,y) : y = x + 1, x ∈ {1,2,3}}. What is the range of R?

A {1,2,3} B {2,3,4} C {1,2,3,4} D {0,1,2}

2

If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is A ∪ B?

A {1, 2, 3, 4, 5, 6} B {3, 4} C {1, 2, 5, 6} D {1, 2}

3

Nida is checking the commutative property for union. If A = {1,2} and B = {2,3}, which is true?

A A ∪ B = B ∪ A B A ∩ B = B ∩ A C Both A and B D Neither A nor B

4

In a class of 30 students, 18 like Math, 15 like Science, and 8 like both. A student is chosen at random. How many like neither Math nor Science?

A 5 B 7 C 8 D 10

5

If R = {(a,1), (b,2), (c,3)}, what is the range of R?

A {a, b, c} B {1, 2, 3} C {a, 1, b, 2, c, 3} D {a, b}

6

If U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, what is A' (complement of A)?

A {4, 5, 6} B {1, 2, 3} C {1, 2, 3, 4, 5, 6} D ∅

7

Sohail has set A = {1,2,3} and set B = {4,5}. How many elements are in A × B?

A 5 B 6 C 8 D 9

8

If A = {1, 3, 5} and B = {2, 4, 6}, what is A ∩ B?

A {1, 2, 3, 4, 5, 6} B ∅ C {1, 3, 5} D {2, 4, 6}

9

If A = {2, 4, 6, 8} and B = {4, 8, 12}, what is A ∪ B?

A {2, 4, 6, 8, 12} B {4, 8} C {2, 6, 12} D {2, 4, 6, 8}

10

If A = {a, b, c} and B = {b, c, d}, what is A ∩ B?

A {a, b, c, d} B {b, c} C {a, d} D {c, d}

11

If A = {1, 2, 3} and B = {2, 3, 4}, what is A - B?

A {1} B {4} C {1, 4} D {2, 3}

12

In a Venn diagram, if set A is completely inside set B, what does that imply?

A A ⊂ B B B ⊂ A C A = B D A and B are disjoint

13

A relation R is defined as R = {(x,y) : y = 2x + 1, x ∈ {1,2,3}}. What is the range of R?

A {3,5,7} B {1,2,3} C {2,4,6} D {1,3,5}

14

Sara is organizing a school event. She has set A = {1,2,3,4} and set B = {3,4,5,6}. She wants to find the elements that are in both sets. What is A ∩ B?

A {1,2} B {3,4} C {5,6} D {1,2,3,4,5,6}

15

In a class of 35 students, 20 like tea, 15 like coffee, and 5 like both. How many like only tea?

A 15 B 10 C 20 D 5

16

Adnan defines a relation R = {(x,y) : y = 2x, x ∈ {1,2,3}}. What is the range of R?

A {1,2,3} B {2,4,6} C {1,2,3,4,5,6} D {0,2,4}

17

What is the domain of R = {(3, 9), (4, 16), (5, 25)}?

A {3, 4, 5} B {9, 16, 25} C {3, 9, 4, 16, 5, 25} D {9, 16}

18

What is the range of the relation R = {(2,4), (3,6), (4,8)}?

A {2, 3, 4} B {4, 6, 8} C {2, 4, 6, 8} D {4, 8}

19

Hina has set A = {1,2,3,4}. She wants to find the number of elements in the power set of A. How many subsets does A have?

A 4 B 8 C 16 D 32

20

What is the union of A = {1, 2, 3} and the empty set?

A {1, 2, 3} B ∅ C {1, 2, 3, ∅} D U

21

Zara is verifying the associative property for sets. She has A = {1}, B = {2}, C = {3}. Which of the following is true?

A (A ∪ B) ∪ C = A ∪ (B ∪ C) B (A ∩ B) ∪ C = A ∩ (B ∪ C) C A ∪ (B ∩ C) = (A ∪ B) ∩ C D A ∩ (B ∪ C) = (A ∩ B) ∪ C

22

What is the complement of the universal set U?

A U B ∅ C U' = U D Undefined

23

If A = {1, 3, 5, 7} and B = {1, 2, 3, 4}, what is A - B?

A {5, 7} B {2, 4} C {1, 3} D {1, 2, 3, 4, 5, 7}

24

If A = {x | x is a vowel in English} and B = {x | x is a letter in 'apple'}, what is A ∩ B?

A {a, e} B {a, p, l, e} C {p, l} D {a}

25

If R = {(2, 4), (3, 6), (4, 8)}, what is the domain of R?

A {2, 3, 4} B {4, 6, 8} C {2, 4, 6, 8} D {6, 8}