Discrete Mathematics & Graph Theory

Explore sets, logic, counting principles, and graph theory. Learn fundamental discrete structures and their applications in computer science, optimization, and problem-solving.

12th Grade

Discrete Math

~90 min

🎮 Interactive Activity: Set Operations Calculator

Perform set operations!

Given:

A = {1, 2, 3}

B = {2, 3, 4}

Find: A ∪ B

Your answer (use set notation):

🎮 Interactive Activity: Combinatorics Calculator

Calculate permutations or combinations!

Given:

n = 5

k = 3

Find: C(5, 3)

Your answer:

1. Set Theory Fundamentals

Understanding Sets

A set is a well-defined collection of distinct objects. Sets are fundamental to discrete mathematics and form the foundation for many mathematical structures.

Set Notation

Roster notation: A = {1, 2, 3} (list elements)

Set-builder: A = $\\{x \\mid x \\text{ is an integer and } 0 < x < 4\\}$

Cardinality: |A| = number of elements in A

Empty set: ∅ = {} (set with no elements)

Example: Set Operations

Given: A = {1, 2, 3}, B = {3, 4, 5}

Union: A ∪ B = {1, 2, 3, 4, 5} (all elements)

Intersection: A ∩ B = {3} (common elements)

Difference: A - B = {1, 2} (in A but not in B)

2. Set Operations and Properties

3. Propositional Logic

4. Counting Principles

5. Graph Theory Basics

6. Trees and Special Graphs

7. Real-World Applications

Frequently Asked Questions

Practice Time!

Practice Quiz

Questions

Correct

Score

What is the union of sets A = {1, 2, 3} and B = {3, 4, 5}?

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

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How many ways can you arrange 5 books on a shelf?

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What is C(5, 2) (combination of 5 choose 2)?

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In a graph, what is the degree of a vertex?

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What is De Morgan's Law for sets?

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What is the formula for permutations P(n, k)?

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What is a connected graph?

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What is the principle of inclusion-exclusion?

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What is a tree in graph theory?

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