Operations on Sets · 4.1.1
Intersection of sets
Students learn to find the intersection of two or more sets, the elements common to all of them, and to express this intersection using different representations such as listing elements, set-builder notation and Venn diagrams, moving fluently between these forms.
The official learning standard (4.1.1)
“Determine and describe the intersection of sets using various representations.”
What it means
Students learn to find the intersection of two or more sets, the elements common to all of them, and to express this intersection using different representations such as listing elements, set-builder notation and Venn diagrams, moving fluently between these forms.
How it is examined
In Paper 1, students identify or list the intersection of given sets from set notation or Venn diagrams as objective items. In Paper 2, questions may require shading the intersection region on a Venn diagram or listing elements after describing sets from a given context.
Worked example
Given the universal set ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, set A = {2, 3, 5, 7} and set 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}.
- Identify elements common to both A and B: only 2 appears in both sets.
- A ∩ B = {2}.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What does it mean if A ∩ B is an empty set?
It means sets A and B share no common elements at all; they are disjoint. On a Venn diagram, this is shown by drawing the circles for A and B without any overlap between them.
Does the order of sets matter when finding an intersection, like A ∩ B versus B ∩ A?
No. Intersection is commutative, so A ∩ B always equals B ∩ A; both give exactly the same set of common elements.
The order the sets are written in the notation does not change the result.
How do I find A ∩ B ∩ C for three sets?
Find elements that appear in all three sets simultaneously. A practical method is to first find A ∩ B, then intersect that result with C; any element remaining must be common to all three original sets.