Mathematics (Core)Exam code: 0580
Set Notation and Probability Diagrams
Probability
Symbols required by the specification
| Symbol | Meaning |
|---|---|
| n(A) | The number of elements in A |
| A′ | The complement of A: everything in ℰ that is not in A |
| ℰ | The universal set |
| A ∪ B | The union of A and B |
| A ∩ B | The intersection of A and B |
- Union collects everything appearing in either set, or in both, and each element is written once
- Intersection keeps only what appears in both sets
- The complement is found by taking the universal set and removing the named set
Worked example
Reading set notation
ℰ = {x : x is an integer, 1 ⩽ x ⩽ 10}, P = {2, 3, 5, 7} and Q = {1, 3, 5, 7, 9}. Write down n(P), P ∩ Q, P ∪ Q and P′.
Solution:
- n(P) counts the elements of P, so n(P) = 4
- P ∩ Q keeps only what is in both: {3, 5, 7}
- P ∪ Q collects everything in either, listing each once: {1, 2, 3, 5, 7, 9}
- P′ removes P from the universal set: {1, 4, 6, 8, 9, 10}