Operations on Sets
Complement of a set
The set of elements in the universal set that are not in a given set, written A′.
| English | Complement of a set |
|---|---|
| Bahasa Melayu | Pelengkap set |
| 中文 | 补集 |
How it is used
If ξ = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 2, 3}, then A′ = {4, 5, 6, 7, 8}. Check: n(A) + n(A′) = 3 + 5 = 8 = n(ξ).
Where it shows up in SPM
In the Operations on Sets chapter (Form 4). Paper 1 asks you to shade or list A′, (A ∩ B)′ or A′ ∩ B; Paper 2 uses De Morgan's laws, e.g.
showing (A ∪ B)′ = A′ ∩ B′ on a Venn diagram.
Don't confuse it with
Open the chapter: Operations on Sets →
Frequently asked questions
What are De Morgan's laws and why do they matter here?
They state (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′. They let you rewrite the complement of a combined set as an expression in A′ and B′, which is often easier to shade or compute in a Venn-diagram question.
What is (A′)′?
It is A itself. Taking the complement twice returns you to the original set, because the elements outside 'everything outside A' are exactly the elements of A.
So (A′)′ = A always.