Operations on Sets · Form 4
Intersection vs union, in plain terms
Intersection (∩) is the 'and' only what two sets share; union (∪) is the 'or' everything that is in either set, counted once.
Intersection means 'in both'
The intersection of A and B, written A ∩ B, is the set of elements that belong to A and to B at the same time. If A = {1, 2, 3, 4} and B = {3, 4, 5}, then A ∩ B = {3, 4}, because only 3 and 4 sit in both sets.
The word that unlocks it is and, the overlap, the common ground the two sets share.
Union means 'in either'
The union A ∪ B is everything that is in A, or in B, or in both, you sweep up all the elements and gather them into one set. For the same two sets, A ∪ B = {1, 2, 3, 4, 5}.
Notice that 3 and 4 appear only once even though they are in both sets, because a set never repeats an element, and that single fact is why n(A ∪ B) is not simply n(A) + n(B).
Telling them apart under pressure
The two symbols look alike and are easy to swap in a rush: ∩ is intersection, ∪ is union, picture ∪ as an open cup that holds everything, so it is the bigger, union one. A quick sense-check catches most errors: an intersection can never be larger than the smaller of the two sets, while a union can never be smaller than the larger set.
If your answer breaks either rule, you have most likely mixed the two up.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I tell whether a word problem wants intersection or union?
Look for the connecting word: 'and'/'both' signals intersection (A∩B), while 'or'/'at least one' signals union (A∪B). If a question asks for students who play both badminton and chess, that's A∩B; if it asks for students who play at least one, that's A∪B.
Why can't I just add n(A) and n(B) to find n(A∪B)?
A common mistake is adding n(A) and n(B) directly, which double-counts the overlap. The correct rule is n(A∪B) = n(A) + n(B) − n(A∩B); always subtract the intersection once so elements shared by both sets aren't counted twice.
How are intersection and union usually tested in the exam?
Exam questions often ask you to shade A∩B or A∪B on a Venn diagram, or to list the elements of each. Shade only the overlapping region for intersection, and shade every region belonging to either set, without double-shading the overlap, for union.