Sets Basics · Beginner (no experience needed)

Sets Explained: Union, Intersection, Subset & Venn Diagrams

Key terms

Set: a clear collection, named with a capital letter: F = {apple, banana, grape}.
Element (member): apple ∈ F (is in F); carrot ∉ F (is not in F).
Roster notation lists the elements: {2, 4, 6, 8}. Set-builder notation gives the rule: {x | x is even, 1 ≤ x ≤ 9}. “|” means such that.
Empty set ∅ or { }: no elements (cats that can fly).
Finite sets can be counted to the end; infinite sets go on forever: {1, 2, 3, …}. Cardinal number n(A) = how many elements.
Equal sets have the same elements; equivalent sets have the same number of elements.
Universal set U: everything in the topic (the rectangle in a Venn diagram).
Subset A ⊆ B: every element of A is in B. Proper subset A ⊂ B: a subset that is smaller.
Union A ∪ B: in A or B. Intersection A ∩ B: in A and B. Disjoint: A ∩ B = ∅.
Complement A′: in U but not in A. Difference A − B: in A but not in B.
Counting a union: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). De Morgan’s laws: (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′.