Sets and Venn diagrams: watch it solved step by step

Union, intersection, difference, symmetric difference and complements of two sets, with a Venn diagram and a counting check. Level: KS4 / University. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: A = {2, 4, 6, 8}, B = {1, 2, 3, 4}, U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

1. The sets. A set is a collection of distinct things. The order does not matter and repeats count once.
2. Union: in A or B (or both). Gather everything that is in at least one set, writing each thing once. The symbol is .
3. Intersection: in both. Keep only what appears in both sets. The symbol is .
4. Difference: in A but not B. Start with A and remove anything that is also in B. The symbol is a backslash.
5. Symmetric difference: in exactly one. Everything in the union except the overlap.
6. Complements (everything in U that is not in the set). The complement of A is what is left of the universal set U after removing A.
7. Check: counting. Adding the sizes of A and B counts the overlap twice, so subtract it once. This is the inclusion–exclusion rule.

Answer: A ∪ B = 1, 2, 3, 4, 6, 8; A ∩ B = 2, 4; A \ B = 6, 8

Practise sets and venn diagrams with problems the Lab marks for you.