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A set is a collection of objects or values grouped together. A subset is a set whose elements all belong to a larger set, shown as A ⊂ B. Free notes.
Set Language, Subsets and Venn Diagrams is part of Use of Symbols and Algebraic Manipulation in IGCSE Edexcel Higher Maths.
1 min
Reading time
27
Lessons in this topic
IGCSE Edexcel Higher
Pathway
Reviewed by Revise Right
Content review
A set is a collection of objects or values grouped together. A subset is a set whose elements all belong to a larger set, shown as A ⊂ B. Free notes.
Use this lesson to stay inside Use of Symbols and Algebraic Manipulation while connecting the detail back to the wider Topic 2: Equations, Formulae and Identities topic.
Read the core explanations from Set Language, Subsets and Venn Diagrams before testing yourself from memory.
Set language is a compact way to describe groups of numbers or objects and the relationships between them.
Venn diagrams make those relationships visible, so the notation and the picture should support each other rather than feel like separate topics.
Worked example: Explaining subset notation
Let A be the set of multiples of 4 and B be the set of even numbers. Explain why A is a subset of B.
Answer: A is a subset of B because every multiple of 4 is even.
Worked example: Reading an intersection
In a class, set A is students who play football and set B is students who play tennis. What does A ∩ B represent?
Answer: The students who play both football and tennis.
Worked example: Counting the Number of Elements in a Venn Diagram
In a class, 14 students are in set A, 11 are in set B and 5 are in both. How many students are in A ∪ B?
Answer: n(A ∪ B) = 20
When you see an overlap in a Venn diagram, think 'both'. When you see a union symbol, think 'in at least one of the sets'.
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-03-25.
Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
A set is a collection of objects or values grouped together. Set notation and Venn diagrams describe the relationships between sets, such as subsets and intersections.
The intersection, A ∩ B, is the elements common to both sets, the overlap of the Venn diagram. The union, A ∪ B, is the elements in at least one of the sets: in A or B or both.
A subset is a set whose elements all belong to a larger set, shown as A ⊂ B. For example, the set of multiples of 4 is a subset of the even numbers, because every multiple of 4 is even. A subset does not mean the sets are equal.
A ∪ B means the union of A and B: the elements in at least one of the sets. If 14 students are in A, 11 in B and 5 in both, then n(A ∪ B) = 9 + 5 + 6 = 20.
A ∩ B means the intersection of sets A and B: the elements in both sets at once. If A is students who play football and B is students who play tennis, A ∩ B is the students who play both.
Start with the intersection, then subtract it from each set to find the only regions, and add them up. If 14 students are in A, 11 in B and 5 in both, A only = 9 and B only = 6, so n(A ∪ B) = 9 + 5 + 6 = 20.
A subset does not mean the sets are equal; it means all the elements of one set belong to a larger set. Treating a subset as if the sets are equal is a common pitfall.
The set of multiples of 4 is a subset of the set of even numbers, because every multiple of 4 is even. In notation, if A is the multiples of 4 and B is the even numbers, A ⊂ B.