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# 16h - Discrete Mathematics Functions 16-2 Previous Lecture...

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Introduction Functions Discrete Mathematics Andrei Bulatov Discrete Mathematics - Functions 16-2 Previous Lecture Properties of binary relations Equivalence relations and partitions Partial and total orders Diagrams of orders square4 reflexivity square4 symmetricity square4 transitivity square4 anti-symmetricity Discrete Mathematics - Functions 16-3 Functions In many instances we assign to each element of a set a particular element of a second set. For example , assign rooms to people in a hotel Or we may assign a grade to each student from a class What we get is a set of pairs (Person, Door) or (Student, Grade), that is a relation, but a very particular one Discrete Mathematics - Functions 16-4 Functions (cntd) A relation R from A to B is called a function from A to B, if for every a A there is exactly one b B such that (a,b) R. (Also mappings , transformations ) Adams Chou Goodfriend Rodriguez Stevens A B C D F We use f,g,h to denote functions f: A B f(a) = b f(Rodriguez) = A Discrete Mathematics - Functions 16-5 Example Consider the function from the set People to People: f(a) = b if b is the father of a. James VI of Scotland Charles I Charles II Mary James II Elizabeth Anne Henry Henrietta William II William III Mary II Anne Henry Frederick Elizabeth Frederick V Sophia (Queen Anne) Rupert Charles Louis Ernest Augustus George I (http://www.royal.gov.uk) Discrete Mathematics - Functions 16-6 Domain and Codomain Let f: A B be a function from A to B.

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