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
Let P = {a, e, i} and Q = {i, o, u}. Then P ∪ Q = {a, e, i, o, u}, all five vowels, with the shared letter i written once.
Where it shows up in SPM
In the Operations on Sets chapter (Form 4). Paper 1 lists or shades the union; Paper 2 applies n(P ∪ Q) = n(P) + n(Q) − n(P ∩ Q) to solve for an unknown given a Venn diagram.
Don't confuse it with
Intersection of sets (∩)Union gathers all elements from both sets; intersection keeps only the ones common to both. Read ∪ as 'or', ∩ as 'and'.
Open the chapter: Operations on Sets →
Frequently asked questions
If A is a subset of B, what is A ∪ B?
It is just B. When A ⊂ B, every element of A is already in B, so combining them adds nothing new.
For A = {2, 4} and B = {1, 2, 3, 4, 5}, A ∪ B = {1, 2, 3, 4, 5} = B.
In a word problem, which words signal union?
Words like 'or', 'at least one', and 'either' usually point to union. 'Students who play football or hockey' means n(F ∪ H).
Watch for 'both', which signals intersection instead.
Related terms
IntersectionThe set of elements that two sets share, written A ∩ B.UnionThe set of all elements in either set, written A ∪ B.ComplementThe set of all elements not in a given set, within the universal set.Venn diagramA drawing using overlapping regions to show the relationships between sets.ElementA member of a set, written with the symbol ∈.