7. Let S = {1,2,3, ...,8}. Let R be the relation on S defined by the following: %3D xRy + xy is a perfect square a. Find all the coordinate pairs in the relation R. b. Draw a directed graph for R. c. If R is an equivalence relation, find all the distinct equivalence classes. If R is not an equivalence relation, state exactly which property(s) it fails and include specific examples.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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7. Let S = {1,2, 3, ..., 8}. Let R be the relation on S defined by the following:
xRy + xy is a perfect square
a. Find all the coordinate pairs in the relation R.
b. Draw a directed graph for R.
c. If R is an equivalence relation, find all the distinct equivalence classes. If R is not
an equivalence relation, state exactly which property(s) it fails and include
specific examples.
Transcribed Image Text:7. Let S = {1,2, 3, ..., 8}. Let R be the relation on S defined by the following: xRy + xy is a perfect square a. Find all the coordinate pairs in the relation R. b. Draw a directed graph for R. c. If R is an equivalence relation, find all the distinct equivalence classes. If R is not an equivalence relation, state exactly which property(s) it fails and include specific examples.
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