A LITTLE PRACTICE, EVERY DAY·GCSE MATHS
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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.

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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

  1. A ∩ B = {6} (only element in both A and B)
  2. A ∪ B = {2,3,4,6,8,9,10} (all elements in A or B)
  3. 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

  1. A ∪ B covers all of circle A and all of circle B (including overlap)
  2. (A ∪ B)' is everything outside both circles
  3. 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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