Explore topic-wise MCQs in Discrete Mathematics.

This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

A partial order ≤ is defined on the set S = {x, b1, b2, … bn, y} as x ≤ bi for all i and bi ≤ y for all i, where n ≥ 1. The number of total orders on the set S which contain the partial order ≤ is ______

A. n+4
B. n2
C. n!
D. 3
Answer» D. 3
Discussion
2.

Consider the ordering relation a | b ⊆ N x N over natural numbers N such that a | b if there exists c belong to N such that a*c=b. Then ___________a) | is an equivalence relationb) It is a total orderc) Every subset of N has an upper bound under |d) (N,

A. | is an equivalence relation
B. It is a total order
C. Every subset of N has an upper bound under |
D. (N,|) is a lattice but not a complete lattice
Answer» E.
Discussion
3.

The inclusion of ______ sets into R = {{1, 2}, {1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5}} is necessary and sufficient to make R a complete lattice under the partial order defined by set containment.

A. {1}, {2, 4}
B. {1}, {1, 2, 3}
C. {1}
D. {1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}
Answer» D. {1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}
Discussion
4.

A partial order P is defined on the set of natural numbers as follows. Here a/b denotes integer division. i)(0, 0) ∊ P. ii)(a, b) ∊ P if and only if a % 10 ≤ b % 10 and (a/10, b/10) ∊ P. Consider the following ordered pairs:i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153)The ordered pairs of natural numbers are contained in P are ______ and ______

A. (145, 265) and (0, 153)
B. ∊ P if and only if a % 10 ≤ b % 10 and (a/10, b/10) ∊ P. Consider the following ordered pairs:i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153)The ordered pairs of natural numbers are contained in P are ______ and ______a) (145, 265) and (0, 153)b) (22, 101) and (0, 153)
C. (101, 22) and (145, 265)
D. (101, 22) and (0, 153)
Answer» E.
Discussion
5.

Suppose X = {a, b, c, d} and π1 is the partition of X, π1 = {{a, b, c}, d}. The number of ordered pairs of the equivalence relations induced by __________

A. 15
B. 10
C. 34
D. 5
Answer» C. 34
Discussion
6.

If the longest chain in a partial order is of length l, then the partial order can be written as _____ disjoint antichains.

A. l2
B. l+1
C. l
D. ll
Answer» D. ll
Discussion
7.

The less-than relation, <, on a set of real numbers is ______

A. not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric
B. a partial ordering since it is asymmetric and reflexive
C. a partial ordering since it is antisymmetric and reflexive
D. not a partial ordering because it is not antisymmetric and reflexive
Answer» B. a partial ordering since it is asymmetric and reflexive
Discussion
8.

Let a set S = {2, 4, 8, 16, 32} and <= be the partial order defined by S <= R if a divides b. Number of edges in the Hasse diagram of is ______

A. 6
B. 5
C. 9
D. 4
Answer» C. 9
Discussion