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Relation on the set of positive integers

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Reference no: EM131083875

Define the following relation on the set of positive integers

xRy if x - y is an even integer 

1.  Show that R is an equivalence relation.

With an equivalence relation, the set on which the relation is defined is divided into subsets called equivalence classes. These subsets consist of all elements that are equivalent to each other. The equivalence class of 1, denoted by [1] consists of all elements that are equivalent to 1 under the relation.

2. How many distinct equivalence classes are there in this example? Can you describe the sets?

Reference no: EM131083875

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