# Equivalence relation on set of ordered pairs

Let S be the set of ordered pairs of positive integers, let z = (5,8), and define R so that (x1, x2) R (y1, y2) means that x1 + y2 = y1 + x2.

Show that the given relation R is an equivalence relation on the set S. Then describe the equivalence class containing the given element z of S, and determine the number of distinct equivalence classes of R.

Solution Summary

A detailed proof of the fact that the given relation R on the set S of all ordered pairs of positive integers is an equivalence relation is provided. The equivalence class containing the given element z is described. A detailed determination of the number of distinct equivalence classes of R is given, as are examples of elements of several different equivalence classes.

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Georgia Martin, PhD

Rating 4.9/5

Active since 2004

AB, Hood College
PhD, The Catholic University of America
PhD, The University of Maryland at College Park

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