What is important to know about Set notation?

ξ = universal set (all elements being considered).

What is important to know about Set notation?

A ∩ B = intersection (in both A and B).

What is important to know about Set notation?

A ∪ B = union (in A or B or both).

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Statistics & Probability · Higher

Set notation

Set notation provides a formal language for describing collections of elements and their relationships. It is used alongside Venn diagrams in probability and logic questions.

Revising set notation the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Set notation GCSE” on the site for the complete guide.

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Key facts to remember

1ξ = universal set (all elements being considered).
2A ∩ B = intersection (in both A and B).
3A ∪ B = union (in A or B or both).
4A' = complement of A (not in A).
5n(A) = number of elements in set A.
6x ∈ A means "x is an element of A"; x ∉ A means "x is not in A".

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Worked examples

Example 1

ξ = {1,2,3,4,5,6,7,8,9,10}, A = {2,4,6,8,10}, B = {3,6,9}. Find A ∩ B, A ∪ B and A'.

Working

A ∩ B = {6} (only element in both A and B)
A ∪ B = {2,3,4,6,8,9,10} (all elements in A or B)
A' = {1,3,5,7,9} (elements in ξ but not in A)

AnswerA ∩ B = {6}; A ∪ B = {2,3,4,6,8,9,10}; A' = {1,3,5,7,9}

Example 2

Shade the region representing (A ∪ B)' on a Venn diagram.

Working

A ∪ B covers all of circle A and all of circle B (including overlap)
(A ∪ B)' is everything outside both circles
Shade the region of ξ that is outside both A and B

AnswerThe region outside both circles (neither A nor B)

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Common mistakes

✗Confusing ∩ (intersection) and ∪ (union) — intersection means "and both", union means "either or both".

✗Finding A' as elements not in ξ instead of elements in ξ but not in A.

✗Including elements outside ξ in a set.

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Exam tips

✓Learn the symbols thoroughly: ∩ (and/both), ∪ (or/either), ' (not/complement), ξ (everything).

✓Use a Venn diagram to visualise set notation questions before writing the answer.

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