Operations on Sets
Union
The set of all elements in either set, written A ∪ B.
| English | Union |
|---|---|
| Bahasa Melayu | Kesatuan |
| 中文 | 并集 |
How it is used
If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}. The shared element 3 is written only once.
Where it shows up in SPM
In the Operations on Sets chapter (Form 4). Paper 1 asks you to list or shade A ∪ B; Paper 2 word problems apply n(A ∪ B) = n(A) + n(B) − n(A ∩ B) to survey data, e.g.
students taking two subjects.
Don't confuse it with
Open the chapter: Operations on Sets →
Frequently asked questions
Do I write elements that appear in both sets twice?
No. In a set each element is listed once, no matter how many sets it belongs to.
For {2, 4, 6} ∪ {4, 6, 8}, write {2, 4, 6, 8}, not {2, 4, 6, 4, 6, 8}. Repeating an element would be marked wrong.
Why does the formula for n(A ∪ B) subtract n(A ∩ B)?
Because adding n(A) and n(B) counts the overlapping elements twice. If n(A) = 15, n(B) = 12 and n(A ∩ B) = 5, then n(A ∪ B) = 15 + 12 − 5 = 22.
Subtracting the overlap once corrects the double count.