d420 Discrete Math: Functions and Relations - Set 2 - Part 1

Test your knowledge of technical writing concepts with these practice questions. Each question includes detailed explanations to help you understand the correct answers.

Question 1: Which of the following is true for an anti-reflexive relation?

Every element in the set is related to itself

No element in the set is related to itself

Every element in the set is related to some other element

Only some elements in the set are related to themselves

Question 2: Which of the following describes De Morgan's Law for ¬(p∧q)?

¬p∨¬q

¬p∧¬q

p∨q

¬p∨q

Question 3: In Boolean algebra, what does the expression A.A simplify to?

¬A

Question 4: Which of the following is an example of a tautology in propositional logic?

p∧¬p

p∨¬p

¬(p∨q)\

p∧q

Question 5: What does the complement of A∨B simplify to in Boolean algebra?

¬A∧¬B

A∧¬B

¬A∨B

¬A∨¬B

Question 6: What is the negation of the biconditional statement p↔q?

p∨¬q

¬(p↔q)

(p∧¬q)∨(¬p∧q)

p∧q

Question 7: What is the result of applying the distributive law to p∧(q∨r)?

(p∧q)∨(p∧r)

(p∨q)∧(p∨r)

p∨(q∧r)

(p∨q)∧r

Question 8: Which of the following is an example of a valid argument form?

p∧¬p→q

p→q,¬q→¬p

p→q,p→r,q∧r→p

p∨q→¬p∧q

Question 9: Which of the following is true for a simple graph?

It contains no parallel edges and no loops

It contains only parallel edges

It contains only loops

It contains parallel edges and loops

Question 10: Which of the following best describes a complete graph?

Every vertex is connected to every other vertex

There is exactly one path between any two vertices

Every vertex has a self-loop

Every edge connects to the same vertex

Question 11: What is the degree sequence of a graph?

A list of vertices in order of increasing degree

A list of edges in order of their lengths

A list of vertices in order of decreasing degree

A list of edges in order of their weights

Question 12: What is a bipartite graph?

A graph where vertices can be divided into two sets such that no edges exist within the same set

A graph where every vertex is connected to every other vertex

A graph that contains loops

A graph that contains parallel edges

Question 13: Which of the following is an example of a reflexive relation on set A?

(a,b)∈A, but (b,a)∉A

(a,a)∈A for all a∈A

(a,b)∈A for all a,b∈A

(a,b)∉A for all a,b∈A

Question 14: Which of the following is an example of a transitive relation?

If a is related to b and b is related to c, then a is related to c

If a is related to b, then b must be related to a

If a is related to b, then a is greater than b

If a is related to b, then a must be equal to b

Question 15: What is the Hasse diagram used for?

To represent a partially ordered set

To represent a connected graph

To represent a matrix

To represent a cyclic graph

Question 16: Which of the following is an example of a strict order?

a<b, but a≥b

a≤b, but a=b

a<b, and there are no self-loops

a≥b, and there are self-loops

Question 17: Which of the following describes an equivalence relation?

Reflexive, symmetric, and transitive

Antisymmetric and transitive

Reflexive and antisymmetric

Symmetric and transitive

Question 18: Which of the following describes a strict partial order?

It is a relation that is antisymmetric and transitive

It is a relation that is reflexive and symmetric

It is a relation that is reflexive and antisymmetric

It is a relation that is symmetric and transitive

Question 19: Which of the following is a characteristic of a directed acyclic graph (DAG)?

It contains no cycles

It contains exactly one cycle

It contains multiple cycles

It contains parallel edges

Question 20: Which of the following is a property of a spanning tree?

It is a subgraph that contains all vertices and has no cycles

It is a subgraph that contains all vertices and has cycles

It is a subgraph that contains only some vertices and has no cycles

It is a subgraph that contains only some vertices and has cycles

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