# Lecture Notes for CMSC 250 - Discrete Structures with Plane at Maryland (UMD)

## Notes Information

 Material Type: Class Note Professor: Plane Class: CMSC 250 - Discrete Structures Subject: Computer Science University: University of Maryland Term: Spring 2004 Keywords: Identity FunctionInfinite SetsBijective FunctionContrapositiveGeneralizedDefinitionsRelationshipPropositionalPossible ValuesComposition      ## Sample Document Text

1 Terminology . Domain: set which holds the values to which we apply the function . Co-domain: set which holds the possible values (results) of the function . Range: set of actual values received when applying the function to the values of the domain Function . A "total" function is a relationship between elements of the domain and elements of the co-domain where each and every element of the domain relates to one and only one value in the co-domain . A "partial" function does not need to map every element of the domain. . f: X fiY - f is the function name - X is the domain - Y is the co-domain - x?X y?Y f sends x to y - f(x) = y f of x ; value of f at x ; image of x under f Formal Definitions . Range of f = {y?Y | \$x ?X, f(x) = y} - where X is the domain and Y is the co-domain . Inverse image of y = {x ?X| f(x) = y} - the set of things that map to y . Arrow Diagrams - Determining if they are functions using the Arrow Diagram 2 Teminology of Functions . E...

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