Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > Mathematics & Statistics

Basic Discrete Mathematics Quiz

Free Practice Quiz & Exam Preparation

Difficulty: Moderate
Questions: 15
Study OutcomesAdditional Reading
3D voxel art representing Basic Discrete Mathematics course content

Boost your learning with our Basic Discrete Mathematics practice quiz, designed to reinforce essential concepts like sets and relations, functions, and basic counting techniques. Dive into challenging questions on recurrence relations, graphs and trees, and matrix algebra to sharpen your problem-solving skills and enhance your understanding of algorithm efficiency in discrete mathematics.

Which of the following best defines a set?
A collection of distinct objects
A group of numbers that are consecutive
A system of equations
A matrix of numbers
Which of the following best describes a function?
A relation where each element of the domain is associated with exactly one element of the codomain
A mapping that assigns multiple values to a single domain element
A process that randomly pairs elements from two sets
An unordered collection of elements
In counting problems, which technique is appropriate when order is not important?
Permutations
Combinations
Cartesian products
Recurrence relations
What is the primary characteristic of a tree in graph theory?
It is an acyclic connected graph
It always contains cycles
It can have isolated vertices
It is a complete graph
Which of the following properties does matrix algebra generally not have?
Associativity of matrix multiplication
Commutativity of matrix multiplication
Distributivity over matrix addition
Existence of inverse for non-singular matrices
Consider the recurrence relation T(n) = T(n-1) + 2 with T(1) = 3. What is the value of T(5)?
11
10
12
13
Which of the following defines an equivalence relation on a set?
A relation that is reflexive, symmetric, and transitive
A relation that is reflexive and antisymmetric
A relation that is only symmetric
A relation that is only transitive
Given the functions f(x) = 2x + 1 and g(x) = x², what is the result of the composition (f ∘ g)(x)?
2x² + 1
x² + 2
2x + 1
4x² + 1
Which principle is typically used to compute the total number of outcomes when making a series of independent choices?
Inclusion-Exclusion Principle
Pigeonhole Principle
Fundamental Counting Principle
Principle of Mathematical Induction
Which algorithm is most appropriate for finding the shortest path in a weighted graph with non-negative edge weights?
Dijkstra's algorithm
Bellman-Ford algorithm
Kruskal's algorithm
Depth-first search
What is the determinant of a 2×2 matrix [[a, b], [c, d]]?
ad - bc
ac - bd
ab - cd
bc - ad
Which proof technique involves verifying a base case and then proving that if a statement holds for an integer k, it holds for k+1?
Proof by contradiction
Mathematical induction
Proof by exhaustion
Direct proof
For a graph represented by an adjacency matrix, which property indicates that the graph is undirected?
The matrix is symmetric
The matrix is diagonal
The matrix has zeros on the main diagonal
The matrix is invertible
What is the relationship between the trace of a square matrix and its eigenvalues?
The trace is equal to the sum of its eigenvalues
The trace is equal to the product of its eigenvalues
The trace equals the maximum eigenvalue
The trace equals the minimum eigenvalue
Which of the following is an example of an antisymmetric relation on a set?
The isomorphism relation on graphs
The parallelism relation between lines in a plane
The subset relation (⊆) on sets
The relation 'has the same birthday as'
0
{"name":"Which of the following best defines a set?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"Which of the following best defines a set?, Which of the following best describes a function?, In counting problems, which technique is appropriate when order is not important?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Analyze sets and relations to determine key properties and operations.
  2. Evaluate functions by examining injectivity, surjectivity, and composition.
  3. Apply counting techniques and recurrence relations to solve combinatorial problems.
  4. Interpret graphs and tree structures to assess connectivity and algorithm efficiency.
  5. Utilize matrix algebra to model and solve discrete mathematical problems.

Basic Discrete Mathematics Additional Reading

Here are some top-notch resources to supercharge your discrete mathematics journey:

  1. Mathematics for Computer Science Dive into MIT's comprehensive course covering sets, relations, functions, counting techniques, recurrence relations, graphs, trees, and matrix algebra. It's a treasure trove of knowledge!
  2. Discrete Mathematics Join Shanghai Jiao Tong University's Coursera course, offering 11 modules on discrete math fundamentals, including algorithms and their efficacy. Perfect for flexible, self-paced learning.
  3. Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics Explore MIT's advanced course delving into graph theory, combinatorics, and their applications. A deep dive for the mathematically adventurous.
  4. Best Online Discrete Mathematics Courses and Programs Discover a curated list of online courses from edX, covering various discrete math topics. A great way to find the perfect course tailored to your needs.
  5. Resources for Discrete Math Check out NYU's compilation of discrete math resources, including textbooks, lecture notes, and problem sets. A handy toolkit for mastering the subject.
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics & Statistics Quizzes

Powered by: Quiz Maker