Decision Mathematics 1 Quizzes - Practice and Prepare for Exams

Question 1

Venn diagrams are useful for representing logical statements, but they have some drawbacks. Which of the following is a limitation of using Venn diagrams?

Accepted Answer

They can become cluttered and difficult to interpret for statements involving many sets.

Answer

They can always accurately represent any logical statement.

Answer

They are only suitable for representing very simple logical statements.

Question 2

If the probability of event A is 0.4 and the probability of event B is 0.6, both being independent events, what's the probability of both A and B occurring?

Accepted Answer

0.24

Answer

0.1

Answer

0.8

Answer

1

Question 3

What is the fundamental difference between deterministic and probabilistic decision problems?

Accepted Answer

Deterministic problems have known outcomes, while probabilistic problems have uncertain outcomes.

Answer

Deterministic problems have multiple solutions, while probabilistic problems have a single solution.

Answer

Deterministic problems can be solved logically, while probabilistic problems require statistical analysis.

Answer

Deterministic problems are inherently more complex than probabilistic problems.

Question 4

Which of the following is a heuristic method employed in solving combinatorial optimization problems?

Accepted Answer

Greedy algorithm

Answer

Linear programming

Answer

Dynamic programming

Answer

Branch and bound

Question 5

What is the primary purpose of conducting a sensitivity analysis in decision-making?

Accepted Answer

To gauge the impact of input value changes on the decision's outcome.

Answer

To identify the optimal solution for a given set of input values.

Answer

To verify the accuracy and validity of the decision model.

Answer

To simplify the decision problem and reduce its complexity.

Question 6

Which of the following is not a fundamental concept covered in Decision Mathematics 1?

Accepted Answer

Probability

Answer

Algebra of sets

Answer

Logic

Answer

Critical path analysis

Question 7

In a weighted graph, the numerical value assigned to an edge denotes:

Accepted Answer

The cost of traversing the edge

Answer

The distance between the connected vertices

Answer

The probability of traversing the edge

Answer

The time taken to traverse the edge

Question 8

Which operation is NOT performed on sets?

Accepted Answer

Multiplication

Answer

Union

Answer

Intersection

Answer

Complement

Question 9

In critical path analysis, which activity is considered critical?

Accepted Answer

Activity with the latest finish time

Answer

Activity with the earliest start time

Answer

Activity with the smallest duration

Answer

Activity with the greatest slack

Question 10

In a shortest path problem, which algorithm is used to find the shortest path between two nodes?

Accepted Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Answer

Floyd-Warshall algorithm

Answer

Prim's algorithm

Question 11

Which operation is NOT applicable to sets?

Accepted Answer

Quotient

Answer

Union

Answer

Intersection

Answer

Difference

Question 12

Express the statement "If it rains, the streets will be wet" in propositional logic.

Accepted Answer

p → q

Answer

p ∧ q

Answer

~p → q

Answer

p ↔ q

Question 13

Which theorem is fundamental to graph theory?

Accepted Answer

Euler's Theorem

Answer

Fermat's Theorem

Answer

Pythagoras' Theorem

Answer

Binomial Theorem

Question 14

The algebra of sets is characterized by the operations:

Accepted Answer

Intersection, union, and complement

Answer

Addition, subtraction, and multiplication

Answer

Sine, cosine, and tangent

Answer

Limits, derivatives, and integrals

Question 15

The primary purpose of critical path analysis in project management is to:

Accepted Answer

Identify critical activities

Answer

Estimate project duration

Answer

Allocate resources

Answer

Control project costs

Question 16

The negation of the statement 'Every horse within the given domain is an animal' is:

Accepted Answer

'Some horses within the given domain are not animals'

Answer

'No horses within the given domain are animals'

Answer

'Every animal within the given domain is a horse'

Answer

'Some animals within the given domain are not horses'

Question 17

In a network within the given domain, a critical path is:

Accepted Answer

The path with the least slack

Answer

The longest path from the start to the end of the network

Answer

The shortest path from the start to the end of the network

Answer

The path with the most slack

Question 18

Which of the following is a valid representation of the intersection of sets A and B within the given universal set?

Accepted Answer

A ∩ B

Answer

A U B

Answer

A - B

Answer

B - A

Question 19

A bipartite graph is a graph where:

Accepted Answer

The vertices can be partitioned into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set

Answer

Every vertex has an even degree

Answer

Every vertex has an odd degree

Answer

The graph is connected

Question 20

Which concept is NOT covered in the Decision Mathematics 1 unit?

Accepted Answer

Linear programming

Answer

Algebra of sets

Answer

Graph theory

Answer

Logic

Question 21

A collection of elements that share similar properties is known as a:

Accepted Answer

Set

Answer

Universe

Answer

Complement

Answer

Subset

Question 22

In a network, the path with the longest duration of activities is referred to as the:

Accepted Answer

Critical path

Answer

Minimum path

Answer

Optimal path

Answer

Feasible path

Question 23

A crucial problem-solving skill developed in Decision Mathematics 1 is:

Accepted Answer

Logical reasoning

Answer

Data analysis

Answer

Trigonometric calculations

Answer

Polynomial manipulation

Question 24

The algorithm used to find the shortest path between two points in a graph is:

Accepted Answer

Dijkstra's algorithm

Answer

Floyd-Warshall algorithm

Answer

Bellman-Ford algorithm

Answer

Prim's algorithm

Question 25

What is NOT an advantage of utilizing set theory in mathematics?

Accepted Answer

It aids in data analysis and management.

Answer

It enables the precise representation of mathematical structures.

Answer

It facilitates logical reasoning and problem-solving.

Answer

It simplifies operations involving complex mathematical entities.

Question 26

Given the sets A = {1, 2, 3} and B = {3, 4, 5}, what is the intersection of sets A and B?

Accepted Answer

{3}

Answer

{1, 2, 3, 4, 5}

Answer

{1, 2, 4, 5}

Answer

{1, 2}

Question 27

Which of the following is a valid form of logical argument?

Accepted Answer

If A then B; not B; therefore not A

Answer

If A then B; B; therefore A

Answer

If A then B; not A; therefore B

Answer

If A then B; B; therefore not A

Question 28

Which of the following is a characteristic of a directed network?

Accepted Answer

Edges have a specific direction

Answer

Edges have no direction

Answer

Edges are weighted

Answer

Edges are unweighted

Question 29

What is a defining characteristic of decision mathematics?

Accepted Answer

Incorporates mathematical tools to address real-world problems

Answer

Emphasis on theoretical concepts over practical applications

Answer

Focus on the development of abstract mathematical structures

Answer

Relies exclusively on computational techniques

Question 30

In the context of decision mathematics, what term is used to describe a situation where multiple goals conflict?

Accepted Answer

Multi-objective problem

Answer

Optimization problem

Answer

Nonlinear problem

Answer

Deterministic problem

Question 31

Let U be the universal set containing all natural numbers, A = {1, 3, 5, 7}, and B = {2, 4, 6, 8}. What is A ∩ B?

Accepted Answer

{}

Answer

{1, 2, 3, 4, 5, 6, 7, 8}

Answer

{1, 3, 5, 7}

Answer

{2, 4, 6, 8}

Question 32

Which of the following is a necessary condition for a set to be countable?

Accepted Answer

It must have the same cardinality as the set of natural numbers

Answer

It must be finite

Answer

It must be a subset of the set of integers

Answer

It must be a superset of the set of rational numbers

Question 33

A network flow problem typically involves what?

Accepted Answer

Optimising the flow of resources through a network

Answer

Finding the shortest path between two nodes in a network

Answer

Determining the maximum capacity of a network

Answer

Identifying bottlenecks in a network

Question 34

Which of the following is NOT a benefit of using critical path analysis?

Accepted Answer

It guarantees the project will be completed on time

Answer

It helps identify potential delays and bottlenecks

Answer

It provides a clear timeline for the project

Answer

It improves communication and coordination among project stakeholders

Question 35

Which operation is not a basic set operation?

Accepted Answer

Permutation

Answer

Union

Answer

Intersection

Answer

Complement

Question 36

In a graph, the degree of a vertex represents:

Accepted Answer

The number of edges connected to it

Answer

The number of adjacent vertices

Answer

The total number of edges in the graph

Answer

The total number of vertices in the graph

Question 37

A defining characteristic of a Hamiltonian circuit is that it:

Accepted Answer

Visits each vertex in the graph precisely once

Answer

Starts and ends at the same vertex

Answer

Utilizes every edge in the graph exactly once

Answer

Has the shortest possible length

Question 38

Which statement accurately describes a deterministic decision matrix?

Accepted Answer

All outcomes are known and quantifiable

Answer

Uncertain outcomes cannot be quantified

Answer

The optimal decision is always evident

Answer

The decision-maker's preferences are irrelevant

Question 39

What is the primary purpose of sensitivity analysis?

Accepted Answer

Examining how input parameter changes affect the recommended decision

Answer

Identifying the most influential factors in decision-making

Answer

Optimizing the decision for every possible scenario

Answer

Finding the absolute best solution to the problem

Question 40

Find the complement of the set {x | x is an even number less than 10} with respect to the universal set U = {x | x is an integer and 0 ≤ x ≤ 10}.

Accepted Answer

{x | x is an odd number less than 10}

Answer

{x | x is an odd number greater than 10}

Answer

{x | x is an even number less than 10}

Answer

{x | x is an even number greater than 10}

Question 41

Which condition is necessary for a network to be considered a tree?

Accepted Answer

It must have no cycles.

Answer

It must be connected.

Answer

It must have n-1 edges, where 'n' is the number of vertices.

Answer

It must be a complete graph.

Question 42

In a project network diagram, the critical path is the path:

Accepted Answer

With the longest duration.

Answer

With the shortest duration.

Answer

That has the most activities.

Answer

That has the fewest activities.

Question 43

In propositional logic, the symbol "¬" primarily represents:

Accepted Answer

Negation

Answer

Conjunction

Answer

Disjunction

Answer

Implication

Question 44

A propositional logic statement is considered to be a tautology if it is true for:

Accepted Answer

All possible combinations of truth values

Answer

Some possible combinations of truth values

Answer

No possible combinations of truth values

Answer

Only some specific combinations of truth values

Question 45

In a network, the critical path is the:

Accepted Answer

Longest path from the source to the sink with the highest total weight

Answer

Shortest path from the source to the sink with the lowest total weight

Answer

Path with the highest total weight

Answer

Path with the lowest total weight

Question 46

A bipartite graph is one in which:

Accepted Answer

The vertices can be partitioned into two disjoint sets such that all edges connect vertices from different sets

Answer

Every vertex has degree 2

Answer

The graph is acyclic

Answer

The graph is connected

Question 47

Which of the following is a characteristic of a valid logical argument?

Accepted Answer

The conclusion follows logically from the premises

Answer

The premises are true

Answer

The argument is persuasive

Answer

The conclusion is true

Question 48

Which of the following is NOT a type of graph used to represent relationships between objects?

Accepted Answer

Flow chart

Answer

Undirected graph

Answer

Directed graph

Answer

Weighted graph

Question 49

Which of the following is NOT a benefit of using critical path analysis in project management?

Accepted Answer

It can guarantee that a project will be completed on time

Answer

It can help to identify potential bottlenecks in a project

Answer

It can help to optimize the schedule of a project

Answer

It can help to reduce the risk of project delays

Question 50

Which of the following is NOT a technique used for solving network problems?

Accepted Answer

Union-find algorithm

Answer

Breadth-first search

Answer

Depth-first search

Answer

Dijkstra's algorithm

Question 51

Which of the following methods for finding the critical path in a project network is probabilistic?

Accepted Answer

PERT

Answer

Critical path method (CPM)

Answer

Gantt chart

Answer

Activity-on-node diagram

Question 52

What does the area of overlap between the sets A and B in a Venn diagram represent?

Accepted Answer

A ∩ B

Answer

A ∪ B

Answer

A - B

Answer

B - A

Question 53

A graph with 6 vertices and 11 edges has a chromatic number of 4. What is the maximum possible number of edges in a subgraph induced by any 4 vertices of the graph?

Accepted Answer

7

Answer

5

Answer

9

Answer

10

Question 54

Which of the following sets represents the universal set in this context?

Accepted Answer

U: All elements under consideration

Answer

Ø: The empty set

Answer

A: Any specific set of elements under consideration

Answer

B: Any subset of elements under consideration

Question 55

The complement of the set A ∩ B is:

Accepted Answer

(A ∪ B)'

Answer

A' ∩ B

Answer

A' ∪ B'

Answer

(A' ∩ B')'

Question 56

Which of the following is a valid bijection between the sets
A = {1, 2, 3}
B = {a, b, c}?

Accepted Answer

(1, a), (2, b), (3, c)

Answer

(a, 1), (b, 2), (c, 3)

Answer

(1, b), (2, c), (3, a)

Answer

(1, a), (2, c), (3, b)

Question 57

The number of subsets of a set with n elements is:

Accepted Answer

2^n

Answer

n^2

Answer

n

Question 58

What is the contrapositive of the statement: "If it rains, the ground is wet"?

Accepted Answer

If the ground is not wet, then it does not rain.

Answer

If it rains, then the ground is wet.

Answer

If it does not rain, then the ground is wet.

Answer

If the ground is wet, then it rains.

Question 59

Which of these describes a connected network?

Accepted Answer

A social network where everyone is connected to at least one other person.

Answer

A collection of separate groups with no connections between them.

Answer

A system of roads with multiple dead ends.

Question 60

In critical path analysis, which task always starts first?

Accepted Answer

The task with the earliest possible start time.

Answer

The task with the longest duration.

Answer

The task with the latest possible start time.

Answer

The task with the most dependencies.

Question 61

Which of the following demonstrates a valid logical argument?

Accepted Answer

If it is sunny, I will go for a walk. It is sunny. Therefore, I will go for a walk.

Answer

If it is sunny, I will go for a walk. I did not go for a walk. Therefore, it was not sunny.

Answer

I went for a walk. Therefore, it is sunny.

Question 62

What defines a Hamiltonian path in a graph?

Accepted Answer

A path that visits every vertex in the graph exactly once.

Answer

A path that starts and ends at the same vertex.

Answer

A path that uses every edge in the graph at least once.

Question 63

In a network flow problem, each edge has a capacity of 1. What is the maximum flow possible from node A to node B?

Accepted Answer

The maximum number of paths from A to B that don't share any nodes.

Answer

The capacity of the edge with the smallest capacity.

Answer

The sum of the capacities of all edges in the network.

Question 64

What is a key benefit of using critical path analysis?

Accepted Answer

It identifies the critical path and the tasks crucial for on-time project completion.

Answer

It guarantees the project will finish within the estimated time frame.