Relations
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09/12/2003 02:50 PM
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Relations
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Relations
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09/12/2003 02:50 PM
Relations
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Let
A
and
B
be sets. A
binary relation from
A
to
B
is a subset of
A
x
B
.
Let
A
= { 1, 2, 3 } and
B
= {
a
,
b
}. Then the following are all
relations from
A
to
B
.
R
= { (1,
a
), (2,
a
), (3,
b
) }
1.
S
= { (1,
a
), (1,
b
), (2,
a
) }
2.
T
= { (3,
a
) }
3.
U
= { (2,
a
), (2,
b
) }
4.
Mathematically, if we want to say that
a
is related to
b
in some
relation
R
then we write
a
R
b
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Relations
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09/12/2003 02:50 PM
Relations
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Let
A
and
B
be sets. A
binary relation from
A
to
B
is a subset of
A
x
B
.
Let
A
= { 1, 2, 3 } and
B
= {
a
,
b
} and let
R
= { (1,
a
), (1,
b
), (3,
a
) }.
We can represent this relation several ways, including listing it as
we have done here. Other ways including using a graph and a chart.
R  a  b 
+++
1  x  x 
2 


3  x 

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Relations
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09/12/2003 02:50 PM
Relations
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A
relation on the set
A
is a relation from
A
to
A
.
Consider the relation
R
= { (
a
,
b
) 
a
divides
b
} on the set
A
={1,2,3,4,5,6}.
R
consists of ordered pairs in which the first
number divides evenly into the second number.