This document discusses functions in discrete mathematical structures. It defines a function as mapping elements from one set to unique elements in another set. A function assigns a single element from the codomain to each element in the domain. An example of a string length function maps strings to their lengths. The document also defines related terms like domain, codomain, image, and pre-image. It provides an example of a grade function and asks the reader to identify the domain, codomain, and range based on given information. Finally, it concludes with discussing functions and provides references for further reading.

1. Functions
Ms. Rachana Pathak
(rachanarpathak@gmail.com)
Assistant Professor, Dept of Computer Science and Engineering
Walchand Institute of Technology, Solapur
(www.witsolapur.org)

2. Learning Outcome
2Walchand Institute of Technology, Solapur
At the end of this session,
Students will be able to explain Functions in Discrete Mathematical
Structures.

3. Definition of a function
• A function takes an element from a set and maps it to a
UNIQUE element in another set
R Z
f
4.3 4
Domain Co-domain
Pre-image of 4
Image of 4.3
f maps R to Z
f(4.3)
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4. Definition
• Given any sets A, B, a function f from (or “mapping”) A to B
(f:AB) is an assignment of exactly one element f(x)B
to each element xA.
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5. Graphical Representation
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f
A B
a b

6. • If f:AB, and f(a)=b (where aA & bB), then:
• A is the domain of f.
• B is the codomain of f.
• b is the image of a under f.
• a is a pre-image of b under f.
• In general, b may have more than one pre-image.
• The range RB of f is {b | a f(a)=b }.
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Terminologies

7. Domain & Co-Domain
1
2
3
4
5
“a”
“bb“
“cccc”
“dd”
“e”
A string length function
A
B
C
D
F
Rachana
Darshana
Namrata
Priyanka
Rushika
A class grade function
Domain Co-domain
A pre-image
of 1
The image
of “a”
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8. Think & Write
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• Suppose that: “f is a function mapping students in this class to
the set of grades {A,B,C,D,E}.”
• At this point, you know f’s codomain is: __________, and its
range is ________.
• Suppose the grades turn out all As and Bs.
• Then the range of f is _________, but its codomain is
__________________.

9. Answer
• Suppose that: “f is a function mapping students in this class to
the set of grades {A,B,C,D,E}.”
• At this point, you know f’s codomain is: __________, and its
range is ________.
• Suppose the grades turn out all As and Bs.
• Then the range of f is _________, but its codomain is
__________________.
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unknown
{A,B,C,D,E}
A,B
{A,B,C,D,E}

10. Conclusion :
In this session, We have studied all about Functions
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11. References
• 1. Discrete mathematical structures with applications to computer science -- J. P.
Tremblay & R. Manohar (MGH International)
• Reference Books:
• 1. Discrete Mathematics with combinatorics and graph theory- S. SANTHA
(CENGAGE Learning)
• 2. Discrete Mathematical Structures – Bernard Kolman, Robert C. Busby (Pearson
Education)
• 3. Discrete mathematics -- Liu (MGH)
11Walchand Institute of Technology, Solapur

12. Thank You !!!
12Walchand Institute of Technology, Solapur