Set notation (Edexcel GCSE Maths): Revision Notes
Set notation
What is a set?
A set is a collection of members (also called elements). These elements can be numbers, words, letters, or any other objects. Sets are fundamental building blocks in mathematics that help us organise and work with groups of related items.
Sets can contain any type of object - numbers, letters, words, or even other sets! The key is that each element in a set is distinct and appears only once.
Two ways to define a set
You can write a set in two different ways, and both methods use curly brackets { } to show that you're defining a set.
Method 1: Listing the elements
Simply write out all the members of the set, separating each one with a comma.
Worked Example: Listing Elements
- A = {onions, carrots, peas}
- B = {13, 14, 15, 16}
This method works well when you have a small number of elements that you can easily list out completely.
Method 2: Using a rule
Describe the pattern or rule that determines which elements belong in the set.
Worked Example: Using Rules
- C = {months with exactly 30 days}
- D = {odd numbers between 10 and 20}
This method is useful when you have many elements or when listing them all would be impractical. Notice that 'June' would be a member of set C, and you could also write set D as {11, 13, 15, 17, 19}.
Important set symbols
Union (∪)
The union of two sets combines all elements from both sets. If an element appears in either set (or both), it belongs to the union.
Key point: Union means "either set" - you include everything that appears in set A, set B, or both.
Intersection (∩)
The intersection of two sets contains only the elements that appear in both sets simultaneously.
Key point: Intersection means "both sets" - an element must be in set A AND in set B to be included.
Universal set (ℰ)
The universal set represents all the elements you are allowed to consider in a particular question or context. It sets the boundaries for what you're working with.
Key point: Think of the universal set as your "universe of possibilities" for that specific problem.
Complement (A')
The complement of set A includes everything that is in the universal set ℰ but is NOT in set A.
Key point: Complement means "everything BUT" - all the elements in your universe except those in the specified set.
Working with Venn diagrams
Venn diagrams are visual representations of sets using circles. They help you see relationships between different sets clearly.
Drawing Venn diagrams
Worked Example: Step-by-Step Venn Diagram Construction
- Label the circles with the set names (e.g., P and Q)
- Write elements that are in both sets in the intersection (overlapping area)
- Fill in the remaining areas with elements that belong to only one set
- Include any leftover elements from the universal set outside the circles
Using Venn diagrams for probability
When working with probability questions involving sets, Venn diagrams help you count elements accurately. Remember that each element in the universal set should appear exactly once in your diagram.
Each element in the universal set should appear exactly once in your diagram - this prevents double-counting and ensures accurate calculations.
Exam tips
Critical Exam Strategies:
- Always use curly brackets when writing sets
- Separate set members with commas
- When asked if an element belongs to an intersection, check that it appears in ALL the relevant sets
- For union questions, include elements that appear in ANY of the sets
- In Venn diagrams, make sure every element from the universal set appears exactly once
- Read questions carefully to identify whether you need union, intersection, or complement
Key Points to Remember:
- A set is a collection of members or elements written in curly brackets
- Union (∪) combines elements from either set
- Intersection (∩) contains elements that belong to both sets
- The universal set (ℰ) includes all elements you can consider
- Complement (A') contains everything in the universal set except elements in set A