Discrete Mathematics

Set Operations

Question 1
Marks : +2 | -2
Pass Ratio : 100%
The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ___________
1010100000
1010101101
1111111100
1111101010
Explanation:
The bit string for the union is the bitwise OR of the bit strings.
Question 2
Marks : +2 | -2
Pass Ratio : 100%
Which of the following two sets are disjoint?
{1, 3, 5} and {1, 3, 6}
{1, 2, 3} and {1, 2, 3}
{1, 3, 5} and {2, 3, 4}
{1, 3, 5} and {2, 4, 6}
Explanation:
Two sets are disjoint if the intersection of two sets is the empty set.
Question 3
Marks : +2 | -2
Pass Ratio : 100%
The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set _____________
{1, 2}
{5, 6}
{2, 5}
{1, 6}
Explanation:
The intersection of the sets A and B, is the set containing those elements that are in both A and B.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
Let Ai = {i, i+1, i+2, …..}. Then set {n, n+1, n+2, n+3, …..} is the _________ of the set Ai.
Union
Intersection
Set Difference
Disjoint
Explanation:
By the definition of the generalized intersection of the set.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________
{1, 2, 6, 1}
{1, 2, 5, 6}
{1, 2, 1, 2}
{1, 5, 6, 3}
Explanation:
The union of the sets A and B, is the set that contains those elements that are either in A or in B.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
The complement of the set A is _____________
A – B
U – A
A – U
B – A
Explanation:
The complement of the set A is the complement of A with respect to U.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
The set difference of the set A with null set is __________
A
null
U
B
Explanation:
The set difference of the set A by the null set denoted by A – {null} is A.
Question 8
Marks : +2 | -2
Pass Ratio : 100%
Two sets are called disjoint if there _____________ is the empty set.
Union
Difference
Intersection
Complement
Explanation:
By the definition of the disjoint set.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
The bit string for the set {2, 4, 6, 8, 10} (with universal set of natural numbers less than or equal to 10) is ____________________
0101010101
1010101010
1010010101
0010010101
Explanation:
The bit string for the set has a one bit in second, fourth, sixth, eighth, tenth positions, and a zero elsewhere.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
The difference of {1, 2, 3} and {1, 2, 5} is the set ____________
{1}
{5}
{3}
{2}
Explanation:
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.