Discrete Mathematics | Hasse Diagrams MCQs

Discrete Mathematics | Hasse Diagrams MCQs: This section contains multiple-choice questions and answers on Hasse Diagrams in Discrete Mathematics.
Submitted by Anushree Goswami, on November 04, 2022

1. The Hasse Diagram provides a complete description of the ______ partial order.

1. Associated
2. Complimentary
3. Supplementary
4. Non-Supplementary

Explanation:

The Hasse Diagram provides a complete description of the associated partial order.

2. Hasse diagram is also called -

1. Ordered Diagram
2. Unordered Diagram
3. Partial Ordered Diagram
4. Partial Unordered Diagram

Explanation:

Hasse diagram is also called an ordered diagram.

3. Creating an equivalent Hasse diagram from a _____ graph of a relation on a set A is very straightforward.

1. Undirected
2. Directed
3. Partial undirected
4. Partial directed

Explanation:

Creating an equivalent Hasse diagram from a directed graph of a relation on a set A is very straightforward.

4. Instead of circles, Hasse diagrams have _____ that represent vertices.

1. Nodes
2. Points
3. Squares
4. Subpoints

Explanation:

Instead of circles, Hasse diagrams have points that represent vertices.

5. Due to the _____ nature of partial orders, in Hasse diagrams, edges between vertices are deleted.

1. Transitive
2. Reflexive
3. Associative
4. Distributive

Explanation:

Due to the reflexive nature of partial orders, in Hasse diagrams, edges between vertices are deleted.

6. Since partial orders are ____, we have aRc in the case of aRb, bRc.

1. Transitive
2. Reflexive
3. Distributive
4. Associative

Explanation:

Since partial orders are transitive, we have aRc in the case of aRb, bRc.

7. In Hasse diagrams, remove the ____ implied by the transitive property, i.e., delete the edge from a to c while keeping the other two edges.

1. Vertices
2. Edges
3. Lines
4. Directed lines

Explanation:

In Hasse diagrams, remove the edges implied by the transitive property, i.e., delete the edge from a to c while keeping the other two edges.

8. The vertex 'b' appears above vertices 'a' if they are connected by an edge, e.g., ___.

1. aRa
2. aRb
3. bRb
4. None

Explanation:

The vertex 'b' appears above vertices 'a' if they are connected by an edge, e.g., aRb.

9. In the Hasse diagram, the arrow may be _____ from the edges.

1. Replaced
2. Omitted
4. None of the above

Explanation:

In the Hasse diagram, the arrow may be omitted from the edges.

10. A subset of a partially ordered set A will be called an upper bound of B if ____ for every y ∈ B.

1. y ≤ x
2. x ≤ y
3. y ≤ R
4. x ≤ R

Explanation:

A subset of a partially ordered set A will be called an upper bound of B if y ≤ x for every y ∈ B.

11. When B is a subset of a partially ordered set A, an element z is referred to as a ____ bound of B.

1. Upper
2. Lower
3. Side
4. Inner

Explanation:

When B is a subset of a partially ordered set A, an element z is referred to as a lower bound of B.

12. In S, M is called an upper bound of A if it succeeds all elements of A, i.e., if x in A ___ M, then M is said to be an upper bound of A.

1. Is equal to
2. Is less than
3. Is greater than
4. None of the above

Explanation:

In S, M is called an upper bound of A if it succeeds all elements of A, i.e., if x in A is equal to M, then M is said to be an upper bound of A.

13. ____ (A) indicates an upper bound of A that precedes all other upper bounds of A.

1. Sup
2. Inf
3. Sub
4. Super

Explanation:

Sup (A) indicates an upper bound of A that precedes all other upper bounds of A.

14. Lower bounds for a subset A of S are defined as elements m in S preceding every element in A, i.e., if, for every y in A, _____.

1. m<=y
2. m>=y
3. m<=A
4. m<=S

Explanation:

Lower bounds for a subset A of S are defined as elements m in S preceding every element in A, i.e., if, for every y in A, m<=y.

15. A lower bound is called the ____ of A if it exceeds all lower bounds of A.

1. Supremum
2. Infimum
3. Side Upper
4. Side Lower

Explanation:

A lower bound is called the infimum of A if it exceeds all lower bounds of A.

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