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

Notes Information

Material Type:Class Note
Professor:Staff
Class:CMSC 250 - Discrete Structures
Subject:Computer Science
University:University of Maryland
Term:Fall 2006
Keywords:
  • Identity Function
  • Infinite Sets
  • Contrapositive
  • Bijective Function
  • Generalized
  • Definitions
  • Propositional
  • Possible Values
  • Composition
  • Inverse Function
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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 ?Y - 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 Terminology of Functions . Equ...

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