Discrete Mathematics

Sets

Question 1
Marks : +2 | -2
Pass Ratio : 100%
The set O of odd positive integers less than 10 can be expressed by _____________
{1, 2, 3}
{1, 3, 5, 7, 9}
{1, 2, 5, 9}
{1, 5, 7, 9, 11}
Explanation:
Odd numbers less than 10 is {1, 3, 5, 7, 9}.
Question 2
Marks : +2 | -2
Pass Ratio : 100%
The set of positive integers is _____________
Infinite
Finite
Subset
Empty
Explanation:
The set of positive integers is not finite.
Question 3
Marks : +2 | -2
Pass Ratio : 100%
What is the Cardinality of the Power set of the set {0, 1, 2}?
8
6
7
9
Explanation:
Power set P ({0, 1, 2}) is the set of all subsets of {0, 1, 2}. Hence, P({0, 1, 2}) = {null, {0}, {1}, {2}, {0, 1}, {0,2}, {1, 2}, {0, 1, 2}}.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
Which of the following two sets are equal?
A = {1, 2} and B = {1}
A = {1, 2} and B = {1, 2, 3}
A = {1, 2, 3} and B = {2, 1, 3}
A = {1, 2, 4} and B = {1, 2, 3}
Explanation:
Two set are equal if and only if they have the same elements.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
What is the cardinality of the set of odd positive integers less than 10?
10
5
3
20
Explanation:
Set S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}. Then, Cardinality of set S = |S| which is 5.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
What is the Cartesian product of A = {1, 2} and B = {a, b}?
{(1, a), (1, b), (2, a), (b, b)}
{(1, 1), (2, 2), (a, a), (b, b)}
{(1, a), (2, a), (1, b), (2, b)}
{(1, 1), (a, a), (2, a), (1, b)}
Explanation:
A subset R of the Cartesian product A x B is a relation from the set A to the set B.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
Power set of empty set has exactly _________ subset.
One
Two
Zero
Three
Explanation:
Power set of null set has exactly one subset which is empty set.
Question 8
Marks : +2 | -2
Pass Ratio : 100%
The Cartesian Product B x A is equal to the Cartesian product A x B.
True
False
Explanation:
Let A = {1, 2} and B = {a, b}. The Cartesian product A x B = {(1, a), (1, b), (2, a), (2, b)} and the Cartesian product B x A = {(a, 1), (a, 2), (b, 1), (b, 2)}. This is not equal to A x B.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
A __________ is an ordered collection of objects.
Relation
Function
Set
Proposition
Explanation:
By the definition of set.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
The members of the set S = {x | x is the square of an integer and x < 100} is ________________
{0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
{0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
{1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
{0, 1, 4, 9, 16, 25, 36, 49, 64, 121}
Explanation:
The set S consists of the square of an integer less than 10.