# 2 3 Venn Diagrams and Set Operations

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```					2.3 Venn Diagrams & Set Operations

Venn diagrams use circles to represent sets.

The universal set, U, contains all elements being discussed.

The complement of a set, A′, is the set of elements that are in U but not in
set A.

Cardinal numbers can be placed in regions of the Venn diagram to indicate
survey results.

The formula for the cardinal # of the union of two sets is:
n (A  B) = n (A) + n (B) – n (A∩B)

If one set is a proper subset of the other, the Venn diagram will have one
circle inside the other. All elements of the inner circle are included in the
outer circle.

If the sets have no common elements, they are disjoint sets. The Venn
diagram will have separate circles that do not touch. No elements of one set
are elements of the other B.

If the sets have some (at least one) elements in common, they are
overlapping sets. The Venn diagram will have circles that overlap or share
a common area.

If the sets have the same elements, they are equal sets. Only one circle is
used in the diagram.

The intersection of sets A & B is the set of elements common to both sets.
A ∩ B = {x/x  A and x  B}

The union of sets A & B is the set of all elements in the sets. If elements
are repeated, list only once in the union.
A  B = {x/x  A or x  B}

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