Quiz 15 – SETs

1. Which of the following represents the null (empty) set? a) {0} b) {} c) {∅} d) A set with one element.

2. Which of the following is an example of a null set? a) The set of even numbers divisible by 2. b) The set of prime numbers less than 2. c) The set of natural numbers between 5 and 6. d) The set of months with 32 days.

3. The set { x : x is a positive integer, x ^2 = 9 } in roster form is: a) {3, -3} b) {9, 3} c) {3} d) {9}

4. The set { 2 , 4 , 6 , 8 , . . . } in set-builder form is: a) {x : x is an even number} b) {x : x is a natural number} c) {x : x is an even natural number} d) {x : x is an integer}

5. The set-builder form of the set A = { 1 , 4 , 9 , 16 , 25 } is: a) {x : x is a prime number} b) {x : x is a perfect square, x < 26 x<26} c) {x : x is a perfect square, x < 30 x<30} d) {x : x is a perfect square of a natural number less than 6}

6. If U = { 1 , 2 , 3 , 4 , 5 , 6 } and A = { 2 , 3 , 5 } , then the complement of A, denoted A ′ , is: a) {2, 3, 5} b) {1, 4, 6} c) U d) ∅

7. The complement of the universal set U is: a) U b) A set with one element. c) The null set (∅) d) The power set of U.

8. If A = { a , b , c } and B = { b , c , d } , then A − B (A difference B) is: a) {b, c} b) {a, d} c) {a} d) {d}

9. If A = { 1 , 2 , 3 } and B = { 2 , 3 , 4 } , then B − A is: a) {1, 4} b) {4} c) {2, 3} d) {1}

10. In a class of 40 students, 25 like mathematics and 20 like physics. If 10 students like both subjects, how many students like neither subject? a) 5 b) 10 c) 15 d) 35

11. In a survey of 100 people, 60 read magazine A, 45 read magazine B, and 25 read both. How many read at least one of the two magazines? a) 25 b) 60 c) 80 d) 105

12. If two sets A and B are disjoint, then A ∩ B is: a) A b) B c) Universal Set d) Null Set

13. The set of all elements that are in A or in B (or in both) is called the: a) Difference of A and B b) Intersection of A and B c) Union of A and B d) Complement of A

14. Which of the following statements is true? a) A set can have repeating elements. b) A set cannot have repeating elements. c) The order of elements in a set matters. d) A set must contain at least two elements.

15. The set { x : x is a vowel in the English alphabet, x is not a vowel } is: a) {a, e, i, o, u} b) {a, e} c) A singleton set. d) A null set.

16. Let U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } . If A = { 2 , 4 , 6 , 8 , 10 } , then which of the following represents A ′ in set-builder form? a) {x : x is an odd number} b) {x : x is an odd natural number less than 10} c) {x : x is an odd natural number less than or equal to 9} d) {x : x is an even number}

17. Out of 50 people, 20 like tea, 30 like coffee, and 5 like both. How many like only tea? a) 20 b) 15 c) 10 d) 5

18. If A = { 1 , 2 , 3 } and B = { 3 , 4 , 5 } , then the number of elements in A ∪ B is: a) 3 b) 5 c) 6 d) 2

19. Which of the following sets is equal to ( A ∪ B ) ′ ? a) A ′ ∪ B ′ b) A ′ ∩ B ′ c) A ∩ B d) A ∪ B A∪B

20. In a group of 60 people, 35 speak Hindi, 27 speak English, and 20 speak neither language. How many people speak both Hindi and English? a) 22 b) 12 c) 32 d) 42