L04-2 - Functions f = A Lecture 12 B Functions f:A B function f from set A to set B associates an element f(a B with an element a A The domain of f

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Functions Lecture 12 A B f ( ) =
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Functions function, f, from set A to set B associates an element , with an element : f AB () f aB . aA The domain of f is A. The codomain of fis B. For every input there is exactly one output.
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Functions
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Functions f(S) = |S| f(string) = length(string) f(student) = student-ID f(x) = is-prime(x)
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1 arrow in A B f ( ) = Injections (one-to-one) is an in jection iff every element of B is f of at most 1 thing : f AB ,. ( ( ) ( ')) ( ')   aa A f af a a a | A | | B |
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Surjections (Onto) A B 1arrow± in is a sur jectioniff every element of B is f of something : f AB f ( ) = .( ) bB a A f a b   | A | | B |
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Bijections A B is a bi jectioniff it is surjection and injection. : f AB f ( ) = exactly one arrow in | A | = | B |
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Functions a. One-to-one, b. Onto, c. One-to-one, d. neither d. Not a Not onto not one-to-one and onto function a1a a1a1 1 b2b1b2b2a2 c3c2c3c3b3 4d3d4d4c4 8
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Function Domain Codomain Injective? Subjective? Bijective?
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This note was uploaded on 04/22/2010 for the course CS 23022 taught by Professor Staff during the Spring '08 term at Kent State.

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L04-2 - Functions f = A Lecture 12 B Functions f:A B function f from set A to set B associates an element f(a B with an element a A The domain of f

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