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CPSC 121
Lecture 32
March 30, 2009
Menu March 30, 2009
Topics:
Functions (cont’d)
Examples
Reading:
Today: Epp 7.1, 7.2 (deﬁnitions)
Next:
Epp 12.1
Lab 8 prep
Reminders:
Assignment 4 due Friday, April 3 (by 17:00)
No labs ﬁnal partweek of classes (April 6–8)
— submit all remaining lab work during the week of March 30–April 3
Tutorials continue through April 8
Final exam Friday, April 17, 7:00pm, SRC A
READ
the WebCT Vista course announcements board
Lecture 31: Recap
A
function
f
from
A
to
B
, denoted
f
:
A
→
B
,
is a subset of
A
×
B
where
∀
a
∈
A,
∃
!
b
∈
B
such that
(
a,b
)
∈
f
NOTE:
∃
!
means “there exists a unique” or “there exists exactly one”
In functional notation, we write
f
(
a
) =
b
x
x
y
y
function
not a function
Bipartite Graph
Let
A
and
B
be ﬁnite sets and let
f
be function from
A
to
B
We can illustrate
f
using a
bipartite graph
representation of
f
:
A
→
B
Recall:
A
=
{
1
,
2
,
4
}
,
B
=
{
a,b,c,d
}
,
f
=
{
(1
,b
)
,
(4
,a
)
,
(2
,a
)
}
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View Full Document A
B
1
2
4
a
b
c
d
NOTE: Epp (page 390) calls a bipartite graph an “Arrow Diagram.”
Bipartite Graph (cont’d)
Each element of
A
and each element of
B
is represented by a labelled
vertex
(a dot)
Each ordered pair,
(
a,b
)
∈
f
, represented by a
directed edge
(an arrow)
Function
We can express what it means to be a function in terms of a bipartite graph
Suppose
f
⊆
A
×
B
is represented as a bipartite graph
f
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This note was uploaded on 01/09/2010 for the course CPSC 121 taught by Professor Belleville during the Spring '08 term at The University of British Columbia.
 Spring '08
 BELLEVILLE

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