Sets, grids and Venn diagrams

Edexcel 1MA1 examines set notation explicitly on Higher tier and uses Venn diagrams on both tiers as a probability tool.

Set notation (Higher only)

• ξ (xi) — the universal set, all elements under consideration.
• A ∪ B — union: elements in A or B (or both).
• A ∩ B — intersection: elements in both A and B.
• A' — complement: elements not in A.
• nA — number of elements in A.
• ∅ — empty set.
• A ⊂ B — A is a (proper) subset of B.

Venn diagrams — fill order

1. Start with the intersection A ∩ B (the centre overlap).
2. Subtract from each circle to fill A only and B only.
3. Subtract the total in the circles from ξ to fill the outside.

Two-way tables vs Venn

A two-way table fits "Yes/No, Yes/No" data; a Venn diagram fits "in A?, in B?" overlaps. Two-way tables are usually clearer when the question asks for conditional probability across rows.

Three-set Venn (Higher only)

For three sets there are 8 regions: ξ outside; A only, B only, C only; A∩B, B∩C, A∩C; A∩B∩C centre. Always fill the centre first, then the pairwise overlaps minus the centre, then each circle's "only" region.

Common Edexcel exam tip

If the question gives n(A ∪ B) instead of an inclusion sum, use n(A ∪ B) = nA + nB − n(A ∩ B).

A1 marks need all four regions correctly labelled on a Venn diagram, including the universal set rectangle.