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Quizzes > Quizzes for Business > Education

Discrete Mathematics Knowledge Assessment Quiz

Test Your Discrete Math Concepts and Skills

Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art depicting a quiz on Discrete Mathematics Knowledge Assessment

Ready to challenge your understanding with a discrete math quiz tailored for deep learning? This Discrete Mathematics Knowledge Assessment is perfect for students and educators seeking a rigorous practice quiz on logic, sets, and graph theory. Upon completion, participants will gain confidence in key concepts and can adjust questions freely in our editor. Dive into this engaging Mathematics Practice Quiz or explore a broader Mathematics Assessment Quiz lineup. For more options, browse all our quizzes.

How many ways are there to choose 2 items from a set of 5 without regard to order?
10
20
8
5
The combination formula C(5,2) calculates the number of ways to choose 2 from 5 without order, which is 5*4/2=10. None of the other options match this calculation.
What is the contrapositive of the implication "if p then q"?
If q then p
If p then q
If not p then not q
If not q then not p
The contrapositive of p ' q is ¬q ' ¬p and is logically equivalent to the original implication. The other forms do not preserve this equivalence.
In a complete undirected graph with 4 vertices, how many edges does it have?
6
4
8
12
A complete graph K₄ has an edge between every pair of 4 vertices, so it has C(4,2)=6 edges. The other numbers do not fit the combination formula for pairs.
What is the union of the sets {1,2} and {2,3}?
{1,2,3}
{1,2}
{2}
{1,3}
The union operation collects all unique elements from both sets, giving {1,2,3}. The other answers omit or duplicate elements incorrectly.
Which of the following relations on the set {1,2,3} is reflexive?
{(1,2),(2,3)}
{(1,1),(2,2)}
{(1,1),(3,3)}
{(1,1),(2,2),(3,3),(1,2)}
A relation is reflexive if every element relates to itself. Only the first relation contains (1,1), (2,2), and (3,3). The others omit at least one required pair.
How many distinct arrangements (permutations) are there of the letters in the word "LEVEL"?
30
120
60
15
The word LEVEL has 5 letters with L repeated twice and E repeated twice, so the count is 5!/(2!2!)=30. The other options ignore or misapply the repetition adjustment.
How many onto functions exist from a 3-element set to a 2-element set?
8
6
2
4
The total functions are 2³=8, but we must exclude the two constant maps that are not onto, giving 8'2=6. The other numbers either over- or under-count.
Is the formula (p ∧ q) ' p a tautology?
Yes
No
Only when p is true
Only when q is false
In every truth assignment, (p ∧ q) implies p holds true because whenever p∧q is true, p is necessarily true. The other options misunderstand implication behavior.
Which condition guarantees that a connected undirected graph has an Euler tour?
Exactly two vertices have odd degree
The graph has no cycles
All vertices have even degree
The graph is bipartite
A connected graph has an Euler tour precisely when every vertex has even degree. Two odd-degree vertices allow an Euler path but not a tour, and the other conditions are not sufficient.
What is the cardinality of the power set of a 4-element set?
4
8
2
16
The power set of an n-element set has 2^n subsets. For n=4, that is 2^4=16. The other numbers correspond to smaller exponents or misunderstandings.
How many nonnegative integer solutions are there to x₝ + x₂ + x₃ = 8?
64
56
45
36
By the stars-and-bars method, the count is C(8+3'1,3'1)=C(10,2)=45. The other values result from incorrect parameter choices in the formula.
Given the relation R={(1,2),(2,3),(3,4)} on {1,2,3,4}, what is R∘R (composition of R with itself)?
{(1,3),(2,4)}
{(1,3)}
{(1,2),(2,3),(3,4)}
{(1,4)}
Composition R∘R contains pairs (a,c) where there is b with (a,b) and (b,c) in R. Those are (1,3) via 1'2'3 and (2,4) via 2'3'4. The others miss one of these.
Solve the recurrence aₙ = aₙ₋₝ + 5 with a₀ = 2. What is a₄?
18
22
20
24
This is an arithmetic sequence with difference 5: a₄ = 2 + 4 - 5 = 22. The other choices reflect off-by-one or miscalculation errors.
Which principle states that every non-empty set of positive integers has a least element?
Pigeonhole principle
Well-ordering principle
Inclusion-exclusion principle
Principle of mathematical induction
The well-ordering principle asserts that any non-empty subset of the naturals has a smallest element. The other principles address different combinatorial or proof concepts.
Which of the following relations on the set of integers is a partial order?
>
addition
≤
The relation ≤ is reflexive, antisymmetric, and transitive, satisfying the definition of a partial order. The others fail one or more required properties.
Given the recurrence T(n)=2T(n/2)+n with T(1)=1, what is the asymptotic growth of T(n)?
Θ(n²)
Θ(n)
Θ(n log n)
Θ(log n)
By the Master Theorem, a=2, b=2, f(n)=n gives n^{log_b a}=n. Since f(n)=Θ(n^c) with c=1 matches n^{log_b a}, we are in the second case yielding Θ(n log n).
How many onto functions are there from a 4-element set to a 3-element set?
18
30
72
36
By inclusion - exclusion, the count is 3^4 '3·2^4 +3·1^4 =81'48+3=36. The other numbers either omit or double-count some cases.
For sets A, B, and C with |A|=10, |B|=12, |C|=8, |A∩B|=4, |A∩C|=3, |B∩C|=5, and |A∩B∩C|=1, what is |A∪B∪C|?
22
19
20
18
By inclusion - exclusion, |A∪B∪C|=10+12+8'4'3'5+1=19. The other sums misapply the pairwise or triple intersection adjustments.
What is the chromatic number of the cycle graph C₇ (7 vertices)?
2
7
4
3
An odd cycle requires three colors for a proper coloring, so χ(C₇)=3. The other values under- or overestimate the minimum coloring needed.
Solve the recurrence aₙ = 2aₙ₋₝ + n with a₀ = 1. Which closed-form expression is correct for aₙ?
3·2❿ + n ' 2
2·2❿ ' n ' 2
3·2❿ ' n ' 2
2❿ + n + 1
The homogeneous solution is C·2❿ and a particular solution is 'n'2, giving aₙ=3·2❿'n'2 after using a₀=1. The other options miscalculate either the homogeneous or particular part.
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Learning Outcomes

  1. Analyse combinatorial problems using fundamental principles
  2. Evaluate logical statements for consistency and validity
  3. Identify structures in graph theory and set theory
  4. Apply counting techniques to solve discrete problems
  5. Demonstrate understanding of relations and functions
  6. Master recurrence relations and induction methods

Cheat Sheet

  1. Fundamental Counting Principles - Dive into the Rule of Sum and the Rule of Product to count outcomes like a boss, whether you're choosing pizza toppings or outfits. Mastering these rules means you can quickly calculate combinations like 3 flavors × 4 crusts = 12 delicious pizzas! Get the crunchy details Discrete Mathematics - Counting Theory
  2. Permutations vs. Combinations - Learn why order makes all the difference when you're lining up friends for a selfie (permutations) versus just picking squad members (combinations). You'll use n!/(n-r)! for order and n!/[r!(n-r)!] for no-order scenarios, turning complex problems into simple calculations. Explore more cool tricks Combinatorics and Graph Theory
  3. De Morgan's Laws - Flip "ands" to "ors" (and vice versa) with a logical twist that makes simplifying boolean expressions feel like solving a mini puzzle. Remember ¬(p ∧ q) ≡ (¬p ∨ ¬q) and ¬(p ∨ q) ≡ (¬p ∧ ¬q) to conquer even the trickiest statements. Practice the magic spells Last Minute Notes - Discrete Mathematics
  4. Set Operations - Get cozy with unions, intersections, and differences as you mix and match sets like a mathematician DJ spinning tracks. A ∪ B throws a party with all elements, A ∩ B spots the VIPs in both groups, and A − B shows who's left out. Remix your set theory skills Last Minute Notes - Discrete Mathematics
  5. Relations and Their Properties - Peek into reflexive, symmetric, antisymmetric, and transitive properties to understand how elements within a set form relationships - sometimes they're best buddies, sometimes not. These concepts unlock the doors to equivalence relations and partial orders, the secret societies of math. Build your social network Last Minute Notes - Discrete Mathematics
  6. Function Types - Discover injective (one-to-one), surjective (onto), and bijective (both!) functions and see how they map elements between sets like perfect matchmakers. Spotting these types helps you solve mapping puzzles in everything from algebra to cryptography. Find your perfect match Last Minute Notes - Discrete Mathematics
  7. Recurrence Relations - Crack the code of sequences defined by their own history, like the Fibonacci chain where each term is the sum of its parents. Unlocking closed-form solutions turns a recursive maze into a straight path to the answer. Trace the sequence path Discrete Math
  8. Mathematical Induction - Use the trusty base case and a solid inductive step to topple infinite dominos of proofs, showing that if one statement holds then the next one will too. It's like proving a rumor is true for all your classmates after whispering it to the first person. Start the chain reaction Discrete Math
  9. Graph Theory Basics - Explore vertices, edges, paths, and cycles to see how networks, maps, and social graphs really work under the hood. Whether you're planning routes or analyzing friendships, these concepts are the building blocks for every networked system. Walk the nodes Discrete Math | Computer Science
  10. Inclusion-Exclusion Principle - Master the art of counting overlapping sets by adding individual sizes and subtracting their intersections, so you never double-count your treasures. For two sets, it's |A| + |B| − |A ∩ B|; for more, the formula expands like a thrill ride! Balance your set theory Concise Study Companion
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