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Introduction
Functions
Discrete Mathematics
Andrei Bulatov
Discrete Mathematics  Functions
162
Previous Lecture
Properties of binary relations
Equivalence relations and partitions
Partial and total orders
Diagrams of orders
s
reflexivity
s
symmetricity
s
transitivity
s
antisymmetricity
Discrete Mathematics  Functions
163
Functions
In many instances we assign to each element of a set a particular
element of a second set.
For example , assign rooms to people in a hotel
Or
we may assign a grade to each student from a class
What we get is a set of pairs
(Person, Door)
or
(Student, Grade),
that is a relation, but a very particular one
Discrete Mathematics  Functions
164
Functions (cntd)
A relation
R
from
A
to
B
is called
a
function
from
A
to
B, if for
every
a
∈
A
there is exactly one
b
∈
B
such that
(a,b)
∈
R. (Also
mappings
,
transformations
)
Adams
Chou
Goodfriend
Rodriguez
Stevens
A
B
C
D
F
We use
f,g,h to denote functions
f: A
→
B
f(a) = b
f(Rodriguez) = A
Discrete Mathematics  Functions
165
Example
Consider the function from the set People to People:
f(a) = b
if
b
is the father of
a.
James VI of Scotland
Charles I
Charles II
Mary
James II Elizabeth
Anne
Henry
Henrietta
Wil iam II
Wil iam III
Mary II
Anne
Henry Frederick
Elizabeth
Frederick V
Sophia (Queen Anne)
Rupert
Charles Louis
Ernest Augustus
George I
(http://www.royal.gov.uk)
Discrete Mathematics  Functions
166
Domain and Codomain
Let
f: A
→
B
be a function from
A
to
B.
Then
A
is called the
domain
of
f,
and
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This note was uploaded on 05/18/2010 for the course MACM MACM 101 taught by Professor Andreibulatov during the Spring '10 term at Simon Fraser.
 Spring '10
 AndreiBulatov

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