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# 16 - LECTURE 16 EQUIVALENCE RELATIONS(8.1-8.3 Relationships...

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LECTURE 16: EQUIVALENCE RELATIONS ( § 8.1-8.3) Relationships of trust depend on our willingness to look not only to our own interests, but also the interests of others. Peter Farquharson He that findeth his life shall lose it: and he that loseth his life for my sake shall find it. Jesus Christ 1. Relations In many things in life, we want to think of objects as being equal. In the eyes of the law, men and women are equal. In terms of gender they are not, but Susie and Anne do have the same gender. In terms of being odd or even, 1 and 3 are equivalent. In terms of being exactly equal, 1 and 3 are different, but 1 and 1 are equal. We need a way to talk about objects being related in some way, and how to consider when objects are equivalent in some way. Let A and B be sets. A relation R from A to B is, at the foundation, a subset of A × B . The elements in this subset tell us when an element from A is related to an element in B . Example 1. Let A = { 1 , 2 , 3 } and B = { x, y, z } .

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16 - LECTURE 16 EQUIVALENCE RELATIONS(8.1-8.3 Relationships...

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