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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.
- Associated
- Complimentary
- Supplementary
- Non-Supplementary
Answer: A) Associated
Explanation:
The Hasse Diagram provides a complete description of the associated partial order.
2. Hasse diagram is also called -
- Ordered Diagram
- Unordered Diagram
- Partial Ordered Diagram
- Partial Unordered Diagram
Answer: A) Ordered 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.
- Undirected
- Directed
- Partial undirected
- Partial directed
Answer: B) 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.
- Nodes
- Points
- Squares
- Subpoints
Answer: B) Points
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.
- Transitive
- Reflexive
- Associative
- Distributive
Answer: B) Reflexive
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.
- Transitive
- Reflexive
- Distributive
- Associative
Answer: A) Transitive
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.
- Vertices
- Edges
- Lines
- Directed lines
Answer: B) Edges
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., ___.
- aRa
- aRb
- bRb
- None
Answer: B) aRb
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.
- Replaced
- Omitted
- Added
- None of the above
Answer: B) Omitted
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.
- y ≤ x
- x ≤ y
- y ≤ R
- x ≤ R
Answer: A) y ≤ x
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.
- Upper
- Lower
- Side
- Inner
Answer: B) Lower
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.
- Is equal to
- Is less than
- Is greater than
- None of the above
Answer: A) Is equal to
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.
- Sup
- Inf
- Sub
- Super
Answer: A) Sup
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, _____.
- m<=y
- m>=y
- m<=A
- m<=S
Answer: A) m<=y
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.
- Supremum
- Infimum
- Side Upper
- Side Lower
Answer: B) Infimum
Explanation:
A lower bound is called the infimum of A if it exceeds all lower bounds of A.