Discrete Mathematics Multiple Choice Questions on “Set Operations”.
1. 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
Clarification: The union of the sets A and B, is the set that contains those elements that are either in A or in B.
2. 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
Clarification: The intersection of the sets A and B, is the set containing those elements that are in both A and B.
3. Two sets are called disjoint if there _____________ is the empty set.
a) Union
b) Difference
c) Intersection
d) Complement
Answer: c
Clarification: By the definition of the disjoint set.
4. 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
Clarification: Two sets are disjoint if the intersection of two sets is the empty set.
5. The difference of {1, 2, 3} and {1, 2, 5} is the set ____________
a) {1}
b) {5}
c) {3}
d) {2}
Answer: c
Clarification: The difference of the sets A and B denoted by A-B, is the set containing those elements that are in A not in B.
6. The complement of the set A is _____________
a) A – B
b) U – A
c) A – U
d) B – A
Answer: b
Clarification: The complement of the set A is the complement of A with respect to U.
7. 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
Clarification: The bit string for the set has a one bit in second, fourth, sixth, eighth, tenth positions, and a zero elsewhere.
8. 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
Clarification: By the definition of the generalized intersection of the set.
9. 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
Clarification: The bit string for the union is the bitwise OR of the bit strings.
10. The set difference of the set A with null set is __________
a) A
b) null
c) U
d) B
Answer: a
Clarification: The set difference of the set A by the null set denoted by A – {null} is A.