Discrete Mathematics
Discrete mathematics studies mathematical structures that are fundamentally countable or finite, including graph theory, logic, sets, and sequences used in computer science.
What You Need to Know
Key Concept Diagram
A graph consists of vertices (nodes) connected by edges
A tree is a connected graph with no cycles
Sets are collections of distinct objects; operations include union, intersection, and complement
Logic uses statements, connectives (AND, OR, NOT), and truth tables
Sequences and series form the basis for algorithm analysis
Key Vocabulary
Graph
A mathematical structure of vertices connected by edges
Vertex
A node or point in a graph
Set
A collection of distinct objects or elements
Truth table
A table showing all possible truth values for a logical expression
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A graph with 5 vertices where every vertex is connected to every other vertex has how many edges?
Question 2
If A = {1, 2, 3} and B = {2, 3, 4}, what is the intersection A ∩ B?
Question 3
What does NOT (p AND q) equal by De Morgan's law?
Key Concepts Summary
- ●A graph consists of vertices (nodes) connected by edges
- ●A tree is a connected graph with no cycles
- ●Sets are collections of distinct objects; operations include union, intersection, and complement
- ●Logic uses statements, connectives (AND, OR, NOT), and truth tables
- ●Sequences and series form the basis for algorithm analysis