Sets and Venn Diagrams: notes

Notation

• Set: a collection of items in curly brackets. A = {2, 4, 6}.
• Element: 4 belongs to A, written 4 in A. n(A) is the number of elements, here 3.
• Universal set: the set of everything being considered, written with the symbol for the universal set.
• Empty set: a set with no elements, written { }. Its number of elements is 0.
• Subset: every element of B is also in A. {2, 4} is a subset of A.

Operations

• Union: elements in A or B or both. Think "everything combined".
• Intersection: elements in both A and B. Think "the overlap".
• Complement: A' is everything in the universal set that is not in A.
• Counting rule: n(A union B) = n(A) + n(B) - n(A intersection B).

Venn Diagrams

• Start in the middle: fill the overlap first, then the rest of each circle, then the outside.
• Check the total: all regions must add to the number in the universal set.
• Example: 30 learners, 18 play soccer, 12 play netball, 5 play both. Only soccer = 13, only netball = 7, both = 5, neither = 30 - 25 = 5.