- 1. What is a Set? Language and Notation
Define a set as a well-defined collection of distinct objects, write sets by listing and by the rule (set-builder) method, and test membership with the element-of symbols.
- 2. Types of Sets: Finite, Infinite, Empty, Singleton
Classify sets by cardinality: finite versus infinite, the empty set, and singleton sets; compute n(A) and avoid the classic traps {0} and {∅}.
- 3. Equal, Equivalent and Universal Sets
Decide whether two sets are equal (identical elements) or equivalent (same cardinality), explain that equal always implies equivalent but not the reverse, and use the universal set U as the agreed universe every other set sits inside.
- 4. Subsets, Proper Subsets and the Power Set
Decide whether A is a subset of B, distinguish membership from subset containment when a set is nested inside another, derive the count of subsets 2^n from independent in/out choices, and define proper subset and the power set.
- 5. Union, Intersection and Disjoint Sets
Find the union and intersection of two sets, read and shade two-set Venn diagrams, and recognise disjoint sets while distinguishing 'not equal' from 'disjoint'.
- 6. The Complement, and Combining Operations
Find the complement of a set relative to a universal set U, guard the trap of treating the complement as unbounded, meet (A union B)' = A' intersect B' through a worked example, and combine complement with union and intersection.
- 7. Counting with Two Sets: Inclusion-Exclusion
Derive and apply n(A union B) = n(A) + n(B) - n(A intersect B), find any one of the four quantities given the other three, and use a region table to solve multi-part counting problems.
- 8. Two-Set Venn Word Problems
Translate word-problem phrases into set regions, fill the overlap first when solving from words, work a full two-set word problem start to finish, and solve an algebra variant.
- 9. Three-Set Venn Diagrams
Name and locate all eight regions of three overlapping sets, fill a three-set Venn diagram from the centre outward, distinguish 'exactly two' from 'at least two', and solve a full three-set word problem.
- 10. Mixed Review & Exam Practice
Consolidate every idea from the unit - notation, types of sets, equal/equivalent, subsets and the power set, the three operations, and two- and three-set counting - at exam pace, and practise spotting planted errors.
