Set operations

Learn what sets are, how to list their elements using curly brace notation, use membership symbols $\in$ and $\notin$, and recognise the empty set $\emptyset$.

Learn the standard number sets $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$, and $\mathbb{R}$, understand their containment relationships, and use superscript notation for restricted sets like $\mathbb{Z}^+$.

Learn to read and write set-builder notation $\{x : \text{condition}\}$ to describe sets by a rule rather than listing elements, and specify domains using $\{x \in S : \text{condition}\}$.

Learn subset notation $\subseteq$ and $\subset$, prove set equality by showing mutual containment, and compute cardinality $|A|$ for finite sets.

Learn how to combine sets using union and intersection operations and visualise these relationships using Venn diagrams.

Learn to compute the complement of a set, apply key properties like double complementation, and use De Morgan's laws to relate complements to unions and intersections.

Learn to identify when a collection of sets forms a partition of a universal set - pairwise disjoint and exhaustive - and recognise common partitions including the complement partition $\{A, A^c\}$.