Operations on Sets · 4.2.1
Union of sets
Students learn to find the union of two or more sets, all elements belonging to at least one of the sets with no repeats, and express this union using different representations such as listing elements, set-builder notation and Venn diagrams.
The official learning standard (4.2.1)
“Determine and describe the union of sets using various representations.”
What it means
Students learn to find the union of two or more sets, all elements belonging to at least one of the sets with no repeats, and express this union using different representations such as listing elements, set-builder notation and Venn diagrams.
How it is examined
In Paper 1, objective items ask students to list or identify the union of given sets from notation or a Venn diagram. In Paper 2, questions may require listing elements of a union derived from a described context, or shading the union region on a Venn diagram.
Worked example
Given ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {2, 3, 5, 7} and B = {2, 4, 6, 8, 10}. Find A ∪ B.
- List the elements of A: {2, 3, 5, 7}.
- List the elements of B: {2, 4, 6, 8, 10}.
- Combine all elements from A and B, writing any common element (2) only once: {2, 3, 4, 5, 6, 7, 8, 10}.
- Arrange in order: A ∪ B = {2, 3, 4, 5, 6, 7, 8, 10}.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Do I need to write repeated elements twice in a union?
No. A set never contains duplicate elements, so when finding A ∪ B, any element common to both A and B is written only once in the final list, even though it belongs to both original sets.
What is the difference between union and intersection?
Union (A ∪ B) collects every element that is in A, or B, or both, a larger or equal-sized set. Intersection (A ∩ B) keeps only elements common to both A and B, a smaller or equal-sized set.
Union is broader; intersection is stricter.
If A is a subset of B, what is A ∪ B?
If every element of A is already in B, then A ∪ B simply equals B, since combining A with B adds nothing new. This is a useful shortcut to recognise before listing out every element manually.