Discrete Mathematics U-2(Theory of Sets)
1. A __________ is an ordered collection of objects.
a) Relation
b) Function
c) Set
d) Proposition
Answer: c
2. The set O of odd positive integers less than 10 can be expressed by _____________
a) {1, 2, 3}
b) {1, 3, 5, 7, 9}
c) {1, 2, 5, 9}
d) {1, 5, 7, 9, 11}
Answer: b
3. Power set of empty set has exactly _________ subset.
a) One
b) Two
c) Zero
d) Three
Answer: a
4. 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: c
5. The Cartesian Product B x A is equal to the Cartesian product A x B.
a) True
b) False
Answer: b
6. What is the cardinality of the set of odd positive integers less than 10?
a) 10
b) 5
c) 3
d) 20
Answer: b
7. 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: c
8. The set of positive integers is _____________
a) Infinite
b) Finite
c) Subset
d) Empty
Answer: a
9. What is the Cardinality of the Power set of the set {0, 1, 2}?
a) 8
b) 6
c) 7
d) 9
Answer: a
10. 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: b
11. The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________
a) {1, 2, 6, 1}
b) {1, 2, 5, 6}
c) {1, 2, 1, 2}
d) {1, 5, 6, 3}
Answer: b
12. The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set _____________
a) {1, 2}
b) {5, 6}
c) {2, 5}
d) {1, 6}
Answer: a
13. Two sets are called disjoint if there _____________ is the empty set.
a) Union
b) Difference
c) Intersection
d) Complement
Answer: c
14. Which of the following two sets are disjoint?
a) {1, 3, 5} and {1, 3, 6}
b) {1, 2, 3} and {1, 2, 3}
c) {1, 3, 5} and {2, 3, 4}
d) {1, 3, 5} and {2, 4, 6}
Answer: d
15. The difference of {1, 2, 3} and {1, 2, 5} is the set ____________
a) {1}
b) {5}
c) {3}
d) {2}
Answer: c
16. The complement of the set A is _____________
a) A – B
b) U – A
c) A – U
d) B – A
Answer: b
17. The bit string for the set {2, 4, 6, 8, 10} (with universal set of natural numbers less than or equal to 10) is ____________________
a) 0101010101
b) 1010101010
c) 1010010101
d) 0010010101
Answer: a
18. Let Ai = {i, i+1, i+2, …..}. Then set {n, n+1, n+2, n+3, …..} is the _________ of the set Ai.
a) Union
b) Intersection
c) Set Difference
d) Disjoint
Answer: b
19. The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ___________
a) 1010100000
b) 1010101101
c) 1111111100
d) 1111101010
Answer: d
20. The set difference of the set A with null set is __________
a) A
b) null
c) U
d) B
Answer: a
21. Let the set A is {1, 2, 3} and B is {2, 3, 4}. Then the number of elements in A U B is?
a) 4
b) 5
c) 6
d) 7
Answer: a
22. Let the set A is {1, 2, 3} and B is { 2, 3, 4}. Then number of elements in A ∩ B is?
a) 1
b) 2
c) 3
d) 4
Answer: b
23. Let the set A is {1, 2, 3} and B is {2, 3, 4}. Then the set A – B is?
a) {1, -4}
b) {1, 2, 3}
c) {1}
d) {2, 3}
Answer: c
24. In which of the following sets A – B is equal to B – A?
a) A = {1, 2, 3}, B = {2, 3, 4}
b) A = {1, 2, 3}, B = {1, 2, 3, 4}
c) A = {1, 2, 3}, B = {2, 3, 1}
d) A = {1, 2, 3, 4, 5, 6}, B = {2, 3, 4, 5, 1}
Answer: c
25. Let A be set of all prime numbers, B be the set of all even prime numbers, C be the set of all odd prime numbers, then which of the following is true?
a) A ≡ B U C
b) B is a singleton set.
c) A ≡ C U {2}
d) All of the mentioned
Answer: d
26. If A has 4 elements B has 8 elements then the minimum and maximum number of elements in A U B are ____________
a) 4, 8
b) 8, 12
c) 4, 12
d) None of the mentioned
Answer: b
27. If A is {{Φ}, {Φ, {Φ}}}, then the power set of A has how many element?
a) 2
b) 4
c) 6
d) 8
Answer: b
28. Two sets A and B contains a and b elements respectively. If power set of A contains 16 more elements than that of B, value of ‘b’ and ‘a’ are _______
a) 4, 5
b) 6, 7
c) 2, 3
d) None of the mentioned
Answer: a
29. Let A be {1, 2, 3, 4}, U be set of all natural numbers, then U-A’(complement of A) is given by set.
a) {1, 2, 3, 4, 5, 6, ….}
b) {5, 6, 7, 8, 9, ……}
c) {1, 2, 3, 4}
d) All of the mentioned
Answer: c
30. Which sets are not empty?
a) {x: x is a even prime greater than 3}
b) {x : x is a multiple of 2 and is odd}
c) {x: x is an even number and x+3 is even}
d) { x: x is a prime number less than 5 and is odd}
Answer: d
