Functions in discrete mathematics

Functions in discrete mathematics

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  Functions Ms. Rachana Pathak (rachanarpathak@gmail.com) AssistantProfessor, Dept of Computer Science and Engineering Walchand Institute of Technology, Solapur (www.witsolapur.org)
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  Learning Outcome 2Walchand Instituteof Technology, Solapur At the end of this session, Students will be able to explain Functions in Discrete Mathematical Structures.
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  Definition of afunction • 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) Walchand Institute of Technology, Solapur 3
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  Definition • Given anysets 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. Walchand Institute of Technology, Solapur 4
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  Graphical Representation Walchand Instituteof Technology, Solapur 5 f A B a b
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  • 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 }. Walchand Institute of Technology, Solapur 6 Terminologies
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  Domain & Co-Domain 1 2 3 4 5 “a” “bb“ “cccc” “dd” “e” Astring 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” Walchand Institute of Technology, Solapur 7
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  Think & Write WalchandInstitute of Technology, Solapur 8 • 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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  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 __________________. Walchand Institute of Technology, Solapur 9 unknown {A,B,C,D,E} A,B {A,B,C,D,E}
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  Conclusion : In thissession, We have studied all about Functions Walchand Institute of Technology, Solapur 10
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  References • 1. Discretemathematical 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
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  Thank You !!! 12WalchandInstitute of Technology, Solapur