Sets and Operations on Sets

Mathematics — First Preparatory

Operations on sets

Operation	Symbol	Definition
Union	A ∪ B	Elements that belong to A or to B (or to both)
Intersection	A ∩ B	Common elements that belong to both A and B
Difference	A − B	Elements that belong to A but not to B
Complement	A′	Elements that belong to U but not to A

When using a Venn diagram, we first place the common elements in the overlapping region of the two circles, then fill the other regions with the remaining elements.
To count the elements of a union we use n(A ∪ B) = n(A) + n(B) − n(A ∩ B). We subtract the intersection because its elements were counted twice when we added the two numbers.

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