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 how to find the set difference of two sets, the elements of one set that are not in another, and rewrite it as an intersection with a complement, including when the sets are built from unions.

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 $\{A, A^c\}$.