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ma2201a17exercises0809.pdf - We discussed relations and...

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We discussed relations and functions. A relation R from A to B is a subset R A × B . A relation on A × A can be reflexive, symmetric or transitive. A relation which is reflexive, symmetric and transitive is called an equivalence relation. An equivalence relation on A × A partitions A into equivalence classes. A relation R A × B is functional if For each a A , there is an element ( a, b ) R . If ( a, b ) R and ( a, b 0 ) R , then b = b 0 . Special kinds of functions are one-to-one and onto. If f : A B is one-to-one then | A | ≤ | B | . If g : A B is onto then | A | ≥ | B | . We counted the number of functions of various kinds from a finite set A to a finite set B . 1. Let A = { a, b, c } and B = { a, c, e, g } . a) How many relations between A and B are there? List three of them. b) How many relations between B and A are there? List three of them. c) List three relations which are both from A to B and from B to A . How many such things are there?
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