There are a variety of ways that we can define our three set operations. The following definition uses set builder notation. Fill in the blanks to complete these definitions.
Assume that
A
\displaystyle {A}
A
and
B
\displaystyle {B}
B
are subsets of the universal set
U
\displaystyle {U}
U
.
A
∩
B
=
{
x
∈
U
∣
x
∈
A
\displaystyle {A}\cap{B}={\left\lbrace{x}\in{U}{\mid}{x}\in{A}\right.}
A
∩
B
=
{
x
∈
U
∣
x
∈
A
?
not
and
or
x
∈
B
}
\displaystyle {x}\in{B}{\rbrace}
x
∈
B
}
.
A
∪
B
=
{
x
∈
U
∣
x
∈
A
\displaystyle {A}\cup{B}={\left\lbrace{x}\in{U}{\mid}{x}\in{A}\right.}
A
∪
B
=
{
x
∈
U
∣
x
∈
A
?
and
or
not
x
∈
B
}
\displaystyle {x}\in{B}{\rbrace}
x
∈
B
}
.
A
′
=
{
x
∈
U
∣
x
\displaystyle {A}'={\left\lbrace{x}\in{U}{\mid}{x}\right.}
A
′
=
{
x
∈
U
∣
x
is
?
not
or
and
in
A
}
\displaystyle {A}{\rbrace}
A
}
.
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