Rensselaer
Electrical, Computer, and Systems Engineering Department
ECSE 4500
Probability for Engineering Applications
Recitation 2
Wednesday Feb. 3, 2010
Sets and Fields
ref. Section 1.4 in Stark and Woods (S&W) text
Set Theory
De
fi
nition:
element
arbitrary, can be anything! often denoted
a, b, c, ...
De
fi
nition:
set
a collection of elements, often denoted
A, B, C, ...
De
fi
nition:
subset
A
⊆
B
means that all elements in
A
are also in
B
.
We say
A
is a subset of
B
.
De
fi
nition:
equality
A
=
B
means
A
⊆
B
and
B
⊆
A.
In words we say
A
equals
B
.
De
fi
nition:
universal set
Ω
the set containing all the elements
De
fi
nition:
null set
φ
the empty set
{}
De
fi
nition:
union
A
∪
B
=
{
set of elements in
either
A or B
}
De
fi
nition:
intersection
A
∩
B
=
{
set of elements in
both
A and B
}
De
fi
nition:
complement
A
c
=
{
set of elements in
Ω
but
not in
A
}
De
fi
nition:
di
ff
erence
A
−
B
=
{
set of elements in A but
not in
B
}
Some Basic Set Identities
Note: to ease the notational burden, we write
A
∩
B
=
AB
as is commonly done in this
fi
eld.
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 Spring '08
 WOODS
 Set Theory, Empty set

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