Sets and Venn Diagrams
A set is a well-defined collection of objects. This lesson develops the language used to describe sets and shows how Venn diagrams turn set relationships into clear pictures.
Learning objectives
After studying these notes, learners should be able to define the main terms, apply the central rules and formulas, solve structured examples and explain each answer clearly.
Key ideas
- Set notation, membership and cardinality
- Finite, infinite, empty, equal and equivalent sets
- Subsets, universal sets and complements
- Union, intersection and disjoint sets
- Two-set and three-set Venn diagram problems
Essential rules and formulas
- n(A union B) = n(A) + n(B) – n(A intersection B)
- A complement contains every element of the universal set that is not in A
- A – B = A intersection B complement
Worked example
If 24 learners study Mathematics, 18 study Physics and 10 study both subjects, then the number studying at least one subject is 24 + 18 – 10 = 32.
Study method
Begin every problem by listing the information supplied and identifying the rule that connects it to the unknown quantity. Keep algebraic steps on separate lines, include units where required and check that the final result is reasonable.
Practice questions
- Represent A union B and A intersection B on Venn diagrams.
- In a class of 40 learners, 25 play football, 19 play volleyball and 8 play both. Find the number who play neither.
- Explain the difference between an empty set and a set containing zero.
Revision checklist
- Can you state each definition without looking at the notes?
- Can you select the correct formula and substitute values accurately?
- Can you explain the reasoning behind each step?
- Can you solve a similar examination question independently?
