Discrete mathematics is a branch of mathematics that focuses on discrete structures, which are distinct and separable values rather than continuous ones. It encompasses key areas such as set theory, logic, combinatorics, graph theory, and algorithms. This field provides essential tools for solving problems in computer science, cryptography, data analysis, and operations research, forming the foundation for understanding digital systems, networks, and efficient computation. Its applications are widespread, from optimizing algorithms in software development to modeling real-world scenarios in engineering and social sciences.
Table of contents
- Part 1: OnlineExamMaker AI quiz generator – The easiest way to make quizzes online
- Part 2: 20 discrete mathematics quiz questions & answers
- Part 3: Automatically generate quiz questions using AI Question Generator
Part 1: OnlineExamMaker AI quiz generator – The easiest way to make quizzes online
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Part 2: 20 discrete mathematics quiz questions & answers
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1. Question: What is the cardinality of the set {1, 2, 3, 4, 5}?
A. 3
B. 4
C. 5
D. 6
Answer: C
Explanation: The set {1, 2, 3, 4, 5} has five distinct elements, so its cardinality is 5.
2. Question: Which of the following is a tautology?
A. p ∧ ¬p
B. p ∨ ¬p
C. p → ¬p
D. ¬p ∧ p
Answer: B
Explanation: The statement p ∨ ¬p is always true for any proposition p, making it a tautology.
3. Question: How many subsets does a set with 3 elements have?
A. 3
B. 6
C. 8
D. 9
Answer: C
Explanation: A set with n elements has 2^n subsets, so for 3 elements, it is 2^3 = 8 subsets.
4. Question: In a graph, what is the degree of a vertex with no edges connected to it?
A. 0
B. 1
C. 2
D. Undefined
Answer: A
Explanation: A vertex with no edges has a degree of 0, as degree is the number of edges incident to it.
5. Question: What is the value of the binomial coefficient C(5, 2)?
A. 5
B. 10
C. 15
D. 20
Answer: B
Explanation: C(5, 2) = 5! / (2! × (5-2)!) = (120) / (2 × 6) = 10.
6. Question: Which relation is both reflexive and symmetric on the set {1, 2}?
A. {(1,1)}
B. {(1,1), (2,2), (1,2)}
C. {(1,2), (2,1)}
D. {(1,1), (2,2)}
Answer: D
Explanation: The relation {(1,1), (2,2)} is reflexive (every element relates to itself) and symmetric (if a relates to b, b relates to a).
7. Question: What is the result of 2^3 in modular arithmetic modulo 5?
A. 1
B. 3
C. 8
D. 13
Answer: B
Explanation: 2^3 = 8, and 8 mod 5 = 3.
8. Question: In logic, what does p ⊕ q represent?
A. p AND q
B. p OR q
C. Exclusive OR (p XOR q)
D. NOT p
Answer: C
Explanation: p ⊕ q is the exclusive OR, true only when p and q have different truth values.
9. Question: How many ways can 3 books be arranged on a shelf?
A. 3
B. 6
C. 9
D. 27
Answer: B
Explanation: The number of permutations of 3 distinct items is 3! = 6.
10. Question: What is the complement of the set A = {1, 2, 3} in the universal set U = {1, 2, 3, 4, 5}?
A. {1, 2, 3}
B. {4, 5}
C. {1, 4, 5}
D. {2, 3, 4}
Answer: B
Explanation: The complement of A is all elements in U not in A, which is {4, 5}.
11. Question: In a complete graph with 4 vertices, how many edges are there?
A. 4
B. 6
C. 8
D. 12
Answer: B
Explanation: A complete graph with n vertices has C(n, 2) edges, so for 4 vertices, C(4, 2) = 6.
12. Question: Which of the following is an equivalence relation on the set {1, 2, 3}?
A. Equality
B. Less than
C. Greater than
D. None of the above
Answer: A
Explanation: Equality is reflexive, symmetric, and transitive, making it an equivalence relation.
13. Question: What is the greatest common divisor (GCD) of 12 and 18?
A. 2
B. 3
C. 6
D. 9
Answer: C
Explanation: The GCD of 12 and 18 is 6, as it is the largest number that divides both.
14. Question: In Boolean algebra, what is the identity element for OR operation?
A. 0
B. 1
C. True
D. False
Answer: A
Explanation: The identity for OR is 0, because x OR 0 = x.
15. Question: How many functions are there from a set with 2 elements to a set with 3 elements?
A. 6
B. 9
C. 12
D. 15
Answer: B
Explanation: For sets of size m and n, the number of functions is n^m, so for m=2 and n=3, it is 3^2 = 9.
16. Question: What is the inverse of the function f(x) = 2x + 1?
A. f^{-1}(x) = x/2 – 1/2
B. f^{-1}(x) = 2x – 1
C. f^{-1}(x) = x + 1/2
D. f^{-1}(x) = (x – 1)/2
Answer: D
Explanation: Solving y = 2x + 1 for x gives x = (y – 1)/2, so f^{-1}(x) = (x – 1)/2.
17. Question: In a tree with 6 vertices, how many edges are there?
A. 5
B. 6
C. 7
D. 8
Answer: A
Explanation: A tree with n vertices has n-1 edges, so for 6 vertices, there are 5 edges.
18. Question: What is the truth value of (p → q) ∧ (q → p) when p is true and q is false?
A. True
B. False
C. Undefined
D. Depends on p
Answer: B
Explanation: p → q is false (true → false), and q → p is true (false → true), so the conjunction is false.
19. Question: How many combinations of 4 items can be chosen from 6?
A. 15
B. 20
C. 30
D. 360
Answer: A
Explanation: C(6, 4) = 6! / (4! × (6-4)!) = 15.
20. Question: Which of the following graphs is bipartite?
A. A cycle with 3 vertices
B. A cycle with 4 vertices
C. A complete graph with 3 vertices
D. A complete graph with 4 vertices
Answer: B
Explanation: A cycle with 4 vertices (C4) is bipartite, as it can be divided into two sets with no intra-set edges.
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