Summary
Set notation is a way to describe collections of objects or numbers that share a common property. Sets are often represented by capital letters and their elements are listed within curly brackets.
- Set — a collection of distinct objects or numbers. Example: A = {1, 2, 3, 4, 5}
- Element — an object or number in a set, denoted by ∈. Example: 3 ∈ A
- Number of Elements (n) — the count of elements in a set. Example: n(A) = 5
- Complement of a Set (A′) — all elements not in the set. Example: If A = {Girls}, then A′ = {Boys}
- Empty Set (∅) — a set with no elements. Example: A = ∅
- Universal Set (U) — a set containing all possible elements. Example: U = {0, 1, 2, 3, 4, 5, 6}
- Subset (⊂) — a set where all elements are contained in another set. Example: If B = {1, 2}, then B ⊂ A
- Union (∪) — a set containing all elements from two sets. Example: A ∪ B
- Intersection (∩) — a set containing only the elements common to two sets. Example: A ∩ B
Exam Tips
Key Definitions to Remember
- A set is a collection of distinct objects.
- An element is a member of a set.
- The empty set (∅) has no elements.
- The universal set contains all possible elements.
- The complement of a set includes elements not in the set.
- The union of sets combines all elements from both sets.
- The intersection of sets includes only common elements.
- A subset is a set whose elements are all in another set.
Common Confusions
- Confusing the union (∪) with intersection (∩).
- Misunderstanding the complement of a set.
- Forgetting that the empty set is a subset of every set.
Typical Exam Questions
- What is A ∪ B? Combine all elements from sets A and B.
- What is A ∩ B? List only the elements common to both sets A and B.
- What is the complement of set A? List all elements not in set A.
What Examiners Usually Test
- Ability to list elements of a set using set notation.
- Understanding of unions, intersections, and complements.
- Ability to solve problems using Venn diagrams.