15 - A = { a 1 ,a 2 ,a 3 ,a 4 } and R = { ( a 1 ,a 2 ) , (...

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However, listing ordered pairs can get tedious and hard to follow. For binary relations R A × B , we have several other representations. 1. (Diagram) Let A = { a 1 ,a 2 } , B = { ( b 1 ,b 2 ,b 3 } , R = { ( a 1 ,b 1 ) , ( a 2 ,b 1 ) , ( a 2 ,b 2 ) } . We can represent R by the following diagram A B b 1 b 2 b 3 a 1 a 2 You should remember this pictorial representation. [We sometimes remove the boundary circles when it is clear which elements belong to which set.] 2. (Directed Graph) In the case where R is a binary relation on A we can also use a directed graph , which consists of a set of nodes correspond- ing to the elements in A , joined by arrowed lines indicating the rela- tionship between the elements. For example, let
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Unformatted text preview: A = { a 1 ,a 2 ,a 3 ,a 4 } and R = { ( a 1 ,a 2 ) , ( a 2 ,a 1 ) , ( a 3 ,a 2 ) , ( a 3 ,a 3 ) } . The directed graph of this relation is A a 1 a 2 a 3 a 4 Notice that the direction of the arrows matters. It is, of course, still possible to use a diagram where the source and target sets are drawn separately as in 1. You should also remember this formulation. [Again, we sometimes omit the boundary circle.] Directed graphs will be stud-ied further in Discrete Maths 2. 16...
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This note was uploaded on 01/02/2010 for the course MATH Math2009 taught by Professor Koskesh during the Spring '09 term at SUNY Empire State.

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