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SPM Mathematics Glossary

Operations on Sets, 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 ∈.Universal setThe set of all elements under consideration, usually drawn as a rectangle.SubsetA set whose every element is also in another set, written ⊂.IntersectionThe set of elements common to two sets, written A ∩ B.UnionThe set of all elements in either set, written A ∪ B.Complement of a setThe set of elements in the universal set that are not in a given set, written A′.

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Frequently asked questions

Which set-operation terms should I learn first?

Start with element, universal set and subset, these describe what a set actually contains and how sets relate to each other. Only after that makes sense should you move to intersection, union and complement, which combine sets using the shorthand symbols ∩, ∪ and a prime or bar.

What is the easiest mix-up in operations on sets?

Intersection (∩, elements in both sets) and union (∪, elements in either set) are mixed up most often, remember ∩ looks like a cap holding only shared elements, while ∪ opens up to collect everything. Complement is also confused with subset, though a complement is defined relative to the universal set.

How do operations-on-sets terms appear in exam questions?

Questions often show a Venn diagram and ask you to shade the region representing A∩B, A∪B or the complement of A, or to list the elements in a given region. Others give set notation directly and ask you to write down or find the number of elements in a set.

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