Sets
Sets is the first SEE Mathematics domain and tests set notation, Venn diagrams, operations (union, intersection, difference, complement), and cardinality word problems. SEE items commonly ask for “only A”, “both”, “neither”, or the number in a labelled Venn region.
Core rules
- Roster form lists elements; set-builder form states a rule. The universal set U contains every element under discussion.
- Two-set cardinality: n(A∪B)=n(A)+n(B)−n(A∩B).
- “Only A” = n(A)−n(A∩B); n(A−B)=n(A)−n(A∩B).
- Complement: n(A′)=n(U)−n(A). It is relative to U.
- Three sets: n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C).
Worked example
In a class of 40, 25 like mathematics, 20 like science, and 10 like both. With M and S, n(M∪S)=25+20−10=35. So 35 like at least one subject and 40−35=5 like neither. Only mathematics =25−10=15. The 10 in both was counted twice in 25+20, so it is subtracted once.
Traps that cost marks
- Giving “both” when the question asks “only one”.
- Forgetting that “neither” is n(U) minus the union.
- Treating A′ as everything outside A but inside A∪B rather than inside U.
- In three-set problems, subtracting all three pairwise intersections and then forgetting to add the triple intersection back.
- Not checking that all Venn regions add to n(U).