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

Answer: A) Associated

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

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.

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

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

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

Answer: B) Reflexive

Explanation:

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


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

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

  1. Vertices
  2. Edges
  3. Lines
  4. 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., ___.

  1. aRa
  2. aRb
  3. bRb
  4. 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.

  1. Replaced
  2. Omitted
  3. Added
  4. 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.

  1. y ≤ x
  2. x ≤ y
  3. y ≤ R
  4. 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.


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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

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.

  1. Is equal to
  2. Is less than
  3. Is greater than
  4. 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.

  1. Sup
  2. Inf
  3. Sub
  4. 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, _____.

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

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

Answer: B) Infimum

Explanation:

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



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