--- title: "Sets & Venn Diagrams" description: "Enumerate sets and their unions and intersections systematically using tables, grids, and Venn diagrams to organise and count outcomes" canonical: https://lightmysky.com/learn/mathematics/sets-and-venn-diagrams-mt_1YwOCMMwD8 source: https://lightmysky.com/learn/mathematics/sets-and-venn-diagrams-mt_1YwOCMMwD8.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Sets & Venn Diagrams Enumerate sets and their unions and intersections systematically using tables, grids, and Venn diagrams to organise and count outcomes Subject: Mathematics · Area: Probability · Ages 12 to 14 Page: https://lightmysky.com/learn/mathematics/sets-and-venn-diagrams-mt_1YwOCMMwD8 ## Ready when they can - List the elements in the union and intersection of two sets using a Venn diagram - Use a two-way table to enumerate all possible outcomes of two combined events - Shade regions of a Venn diagram to represent A ∪ B, A ∩ B, and A′ (complement) ## Lesson: Venn diagrams and tables for sets A set is a group of things, like all your friends who play soccer. When you have two sets, you can draw them as two overlapping circles. That picture is called a Venn diagram. Where the circles overlap, you get things that belong to both sets. You have already counted the four regions of a Venn diagram: only A, only B, both, and neither. You also know about complementary events, things that are 'not this one.' A set works the same way: the complement of a set is everything outside its circle. *(drawing: A table with 6 rows and 6 columns lists every way two dice can land: all 36 outcomes, none missed and none repeated.)* **Example.** To list every outcome of two events, use a two-way table. For two dice, write the first die's numbers 1 to 6 down the side and the second die's numbers 1 to 6 across the top. Each cell is one pair, so there are 6 × 6 = 36 cells, with no pair missed and none repeated. To count the pairs with a total of 4, scan the cells: (1,3), (2,2) and (3,1). That is 3 outcomes out of 36. **Example.** Set A is numbers you say counting by 4, up to 24: {4, 8, 12, 16, 20, 24}. Set B is numbers you say counting by 6, up to 24: {6, 12, 18, 24}. The union, A ∪ B, lists every number in either set: {4, 6, 8, 12, 16, 18, 20, 24}. The intersection, A ∩ B, lists only the numbers in both sets: {12, 24}. When you shade a Venn diagram: shade both whole circles for A ∪ B, shade only the middle overlap for A ∩ B, and shade everything outside a circle for its complement, A′. **Recap.** A Venn diagram or a two-way table lets you list every outcome exactly once, so you can count unions, intersections, and complements without missing anything or doubling up. ## Practice 18 questions on this page, each with its working shown. ## Needs first - [Venn Diagrams and Counting Outcomes](https://lightmysky.com/learn/mathematics/venn-diagrams-and-counting-outcomes-mt_eSv_w46u6H) - [Two-Way Tables](https://lightmysky.com/learn/mathematics/two-way-tables-mt_oD1Rgg52n3) - [Complementary events](https://lightmysky.com/learn/mathematics/complementary-events-mt_XfyqXLqzpx) ## Opens up - [Tree diagrams](https://lightmysky.com/learn/mathematics/tree-diagrams-mt_GDtFU5fyUv) - [Inclusion-Exclusion](https://lightmysky.com/learn/mathematics/inclusion-exclusion-mt_MgU-IMpVHA) - [Conditional Probability from Tables and Venn Diagrams](https://lightmysky.com/learn/mathematics/conditional-probability-from-tables-and-venn-diagrams-mt_Vx88ugViYP)