集合

A set is written with braces $\{\}$ listing its elements. For example $A=\{a,b,d,f,h\}$ is the set whose five elements are $a,b,d,f,h$. We write $a\in A$ to mean that $a$ is an element of $A$.

The union $A\cup B$ is the set of elements that are in $A$ or $B$ (or both). The intersection $A\cap B$ is the set of elements that are in both $A$ and $B$.

Given a universal set $U$, the complement $A^{\prime }$ (or $A^c$) is the set of elements not in $A$. If every element of $A$ is also in $B$, then $A$ is a subset of $B$, written $A\subseteq B$. A set with no elements is the empty set, written $\varnothing$.

When $\cup$ and $\cap$ are mixed, work out the brackets first. For example, for $(A\cap B)\cup C$ find $A\cap B$ first, then take its union with $C$. For $A\cap (B\cup C)$ find $B\cup C$ first.

The 0580 syllabus (for 2025–2027) lists this notation: $n(A)$ (number of elements in $A$), $\in$ / $\notin$ (is / is not an element of), $A^{\prime }$ (complement), $\varnothing$ (empty set), $A\subseteq B$ / $A⊈B$ (is / is not a subset of), $A\cup B$ and $A\cap B$. In the exam the universal set is written with a script E (ℰ) rather than $U$. Core uses $n(A)$, $A^{\prime }$, the universal set, $\cup$ and $\cap$; the rest is Extended notation.

Venn diagrams are limited to two sets in Core and to two or three sets in Extended. In a two-circle diagram, the overlap is $A\cap B$, both circles together are $A\cup B$, and the region outside both circles is $(A\cup B{)}^{\prime }$. For counting questions, fill in the overlap first so that nothing is counted twice.

Proper subsets ($\subset$) were removed from 0580 from 2025. Sets are not a topic in IGCSE Additional Mathematics (0606, 2025–2027) or in A-Level Mathematics (9709).