Discrete Mathematics: Sets, Relations & Logic Cheat Sheet

1. Set Theory Fundamentals

A set is a well-defined collection of distinct objects. Universal Set ($U$), Empty Set ($\emptyset$).

• Union ($A \cup B$): Elements belonging to $A$ or $B$ or both.
• Intersection ($A \cap B$): Elements common to both $A$ and $B$.
• De Morgan’s Laws: $(A \cup B)' = A' \cap B'$ and $(A \cap B)' = A' \cup B'$.

2. Matrix Operations & Determinants

A rectangular arrangement of numbers in rows and columns. Symmetric Matrix ($A = A^T$), Skew-Symmetric Matrix ($A = -A^T$).