Lecture Notes 6

# Lecture Notes 6 - Relations...

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Relations 1 of 1 09/12/2003 02:50 PM prev | slides | next Relations 1 2 3 4 5 6 7 8 9 10 11 12 13 Relations 1 of 1 09/12/2003 02:50 PM Relations prev | slides | next Let A and B be sets. A binary relation from A to B is a subset of A x B . Let A = { 1, 2, 3 } and B = { a , b }. Then the following are all relations from A to B . R = { (1, a ), (2, a ), (3, b ) } 1. S = { (1, a ), (1, b ), (2, a ) } 2. T = { (3, a ) } 3. U = { (2, a ), (2, b ) } 4. Mathematically, if we want to say that a is related to b in some relation R then we write a R b 1 2 3 4 5 6 7 8 9 10 11 12 13 Relations 1 of 1 09/12/2003 02:50 PM Relations prev | slides | next Let A and B be sets. A binary relation from A to B is a subset of A x B . Let A = { 1, 2, 3 } and B = { a , b } and let R = { (1, a ), (1, b ), (3, a ) }. We can represent this relation several ways, including listing it as we have done here. Other ways including using a graph and a chart. R | a | b | ---+---+---+ 1 | x | x | 2 | | | 3 | x | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Relations 1 of 1 09/12/2003 02:50 PM Relations prev | slides | next A relation on the set A is a relation from A to A . Consider the relation R = { ( a , b ) | a divides b } on the set A ={1,2,3,4,5,6}. R consists of ordered pairs in which the first number divides evenly into the second number.

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