Set language and notation

• A set is a well-defined collection of elements, written in curly brackets { }.
• ∪ is union (in A or B or both), ∩ is intersection (in both), ∈ means “is an element of”, ∉ means “is not an element of”.
• ℰ (also written ξ) is the universal set; ∅ is the empty set; A′ is the complement of A.
• Venn diagrams show sets as overlapping regions inside a rectangle for ℰ.
• Higher: sets defined in algebraic terms, subsets (⊂), n(A), and Venn diagrams counting numbers of elements in practical problems.

Elements in curly brackets

A set is a collection of objects, called elements or members. A set can be listed, A = {2, 4, 6, 8}, or described, A = {even numbers between 1 and 9}. Order does not matter and each element is listed once.

Or, and, belongs to

Everything, and nothing

The universal set, ℰ (also written ξ), contains every element being considered in the question. The empty set, ∅ or { }, has no elements. Two sets with no elements in common have an intersection equal to ∅.

A′ means “not in A”

The complement of A, written A′, is every element of ℰ that is not in A. Brackets matter: (A ∪ B)′ is outside both circles; A′ ∪ B′ is everything except the overlap.

Four regions for two sets

In a Venn diagram, a rectangle represents ℰ and each set is a circle inside it. With two overlapping circles there are four regions. Name a region by the conditions that describe it, then fill the overlap first.

{x : …} and ⊂