Operations on Sets
Universal set
The set of all elements under consideration, usually drawn as a rectangle.
| English | Universal set |
|---|---|
| Bahasa Melayu | Set semesta |
| 中文 | 全集 |
How it is used
In a class of 40 pupils, let ξ be all 40 pupils. If A = {pupils who play chess} with n(A) = 12, then A′ = {pupils who do not play chess} and n(A′) = 40 − 12 = 28.
Where it shows up in SPM
In the Operations on Sets chapter (Form 4). The universal set is the rectangle enclosing every Venn diagram; Paper 2 problems state ξ so that complements and 'neither' regions can be worked out.
Don't confuse it with
Open the chapter: Operations on Sets →
Frequently asked questions
Why do we need a universal set at all?
Because a complement has no meaning without it. 'Everything not in A' must be measured against some boundary, and ξ sets that boundary.
Change ξ and A′ changes too, even though A stays the same.
Is the symbol always ξ?
In SPM Mathematics the universal set is usually written ξ (the Greek letter xi), and it is drawn as the outer rectangle. Some books use U, but a KSSM question will show ξ, so use it in your answers.