Operations on Sets
Complement
The set of all elements not in a given set, within the universal set.
| English | Complement |
|---|---|
| Bahasa Melayu | Pelengkap |
| 中文 | 补集 |
How it is used
If the universal set ξ = {1, 2, 3, …, 10} and A = {2, 4, 6, 8, 10}, then A′ = {1, 3, 5, 7, 9}, every element of ξ that is not in A.
Where it shows up in SPM
In the Operations on Sets chapter (Form 4). Paper 1 asks you to shade A′ or (A ∪ B)′ on a Venn diagram; Paper 2 uses complements with De Morgan's laws, e.g.
(A ∩ B)′ = A′ ∪ B′.
Don't confuse it with
Open the chapter: Operations on Sets →
Frequently asked questions
What is the difference between A′ and ξ?
ξ is everything under consideration; A′ is only the part of ξ outside A. Together A and A′ fill ξ exactly, so n(A) + n(A′) = n(ξ).
If n(ξ) = 40 and n(A) = 25, then n(A′) = 15.
What does the complement look like on a Venn diagram?
You shade everything inside the rectangle (ξ) except the circle for A. For (A ∪ B)′, shade only the region outside both circles.
Reading the shading correctly is the key skill Paper 1 tests here.