epdf.pub_the-nuts-and-bolts-of-proofs-third-edition-an-intr

Special Kinds of Theorems 71
To construct more interesting examples, we will consider two operations
between sets.
Given two sets, A and B, their union is the set represented by AU B, and
defined as:
AUB =
{x\xeAorxeB}.
Given two sets, A and B, their intersection is the set represented hy
and defined as:
AnB,
AnB
= {x\x G A and x e B}.
"Venn diagrams" (John Venn [1834-1923] was a British logician) are
commonly used to illustrate properties and operations between sets. Usually
sets are represented by discs, which are labeled and placed inside a bigger
rectangle that represents the universal set U.
Because a Venn diagram is a visual example, it is a good idea to try to
represent a general situation and have sets overlapping each other, as shown
in Diagram 1:
Diagram 1
The shaded area in Diagram 2 represents the set AU B:
Diagram 2