Discrete Mathematics & Math MCQ
Test your Discrete Mathematics & Math knowledge with 100 multiple choice questions covering fundamentals to advanced concepts, with instant feedback and explanations.
What is a set?
2What is the power set of {1,2}?
3What is a proposition in logic?
4What is the truth value of p ∧ q when p=T and q=F?
5What is De Morgan's Law?
6What is a function in mathematics?
7What is the difference between injective (one-to-one) and surjective (onto) functions?
8What is mathematical induction?
9What is a graph in discrete mathematics?
10What is a tree in graph theory?
11What is a relation?
12What is an equivalence relation?
13What is the Pigeonhole Principle?
14What is a permutation?
15What is a combination?
16What is the complement of a set A?
17What is modular arithmetic?
18What is a Boolean algebra?
19What is a Hamiltonian path/circuit in graph theory?
20What is an Euler path in graph theory?
21What is graph coloring?
22What is the GCD (Greatest Common Divisor)?
23What is the LCM (Least Common Multiple)?
24What is a prime number?
25What is a binary number system?
26What is a valid argument in propositional logic?
27What is a tautology in logic?
28What is a recursive definition?
29What is a lattice in discrete mathematics?
30What is the principle of inclusion-exclusion?
31What is a bijection?
32What is Euler's formula for planar graphs?
33What is a sequence?
34What is a generating function?
35What is the floor and ceiling function?
36What is Bayes' theorem?
37What is Big O notation informally?
38What are the four basic operations on sets?
39What is a bipartite graph?
40What is a recurrence relation?
What is the Chinese Remainder Theorem (CRT)?
2What is Fermat's Little Theorem?
3What is Euler's totient function φ(n)?
4What is a partial order?
5What is the Master Theorem?
6What is strong induction vs weak induction?
7What is the inclusion-exclusion principle for derangements?
8What is the Stirling number of the second kind S(n,k)?
9What is Cayley's formula?
10What is Kirchhoff's matrix tree theorem?
11What is a formal language in discrete mathematics?
12What is the Principle of Mathematical Induction and Well-Ordering?
13What is a graph's chromatic polynomial?
14What is the Ramsey number R(m,n)?
15What is the difference between countable and uncountable infinity?
16What is a generating function approach to Fibonacci numbers?
17What is Zorn's Lemma?
18What is the handshaking lemma in graph theory?
19What is the four color theorem?
20What is the Fundamental Theorem of Arithmetic?
21What is a Boolean function and its normal forms?
22What is Stirling's approximation?
23What is a poset and what is Dilworth's theorem?
24How many distinct ways can you arrange the letters of the word "LEVEL"?
25Using proof by contradiction, what assumption do you start with to prove "√2 is irrational"?
26In a connected simple graph with 7 vertices, what is the minimum number of edges required for the graph to remain connected?
27What does it mean for a relation R on set A to be antisymmetric?
28How many different committees of 4 people can be formed from a group of 10 people, if two specific people refuse to serve together?
29What is the chromatic number of a cycle graph C₅ (a 5-vertex cycle)?
30Using the Euclidean algorithm, what is gcd(252, 105)?
31What technique is typically used to solve a linear homogeneous recurrence relation like a_n = 5a_{n-1} - 6a_{n-2}?
32In propositional logic, what is the contrapositive of "If it rains, then the ground is wet"?
33How many onto (surjective) functions are there from a 4-element set to a 2-element set?
34Which of the following degree sequences could NOT belong to any simple graph?
35What is the value of C(n,0) + C(n,1) + C(n,2) + ... + C(n,n)?
36Which proof technique would you use to show that every integer greater than 1 has a prime factor, by assuming a smallest counterexample exists?
37In how many ways can 5 distinct books be distributed among 3 distinct shelves, if each shelf may hold any number of books (including zero)?
38What does Kruskal's algorithm compute, and what greedy rule does it follow?
39What is the multiplicative inverse of 3 modulo 7?
40What is the negation of the statement "For all x, there exists a y such that x + y = 0"?
What is the Axiom of Choice and its significance?
2What is the Gödel incompleteness theorem?
3What is Ramsey Theory's general principle?
4What is the Lovász Local Lemma (LLL)?
5What is the probabilistic method in combinatorics?
6What is algebraic graph theory's spectral theory?
7What is the Tutte polynomial?
8What is the probabilistic analysis of quicksort?
9What is the polynomial hierarchy in descriptive complexity?
10What is the algebraic structure of RSA and why it works?
11What is the Bonferroni inequalities and their use in probability?
12What is the matrix-tree theorem and its connection to random walks?
13What is a matroid and its connection to greedy algorithms?
14What are category theory's functors and natural transformations?
15What is the Lovász theta function and its applications?
16What is the connection between Boolean functions and algebraic normal form?
17What is the Möbius function in combinatorics?
18What is Szemerédi's regularity lemma and its impact?
19Why is the discrete logarithm problem considered hard, and how does it underpin Diffie-Hellman key exchange?
20When solving the non-homogeneous recurrence a_n = 2a_{n-1} + 2ⁿ by the method of undetermined coefficients, why must the trial particular solution be A·n·2ⁿ rather than simply A·2ⁿ?