Let A = {1, 2, 3, 4, 5, 6, 7, 8}. Define a relation R on A by aRb if and only if 3 divides a − b for all a, b ∈ A. Show that R is an equivalence relation on A. Find the equivalence classes [1], [2], [3], and [4].
Let A = {1, 2, 3, 4, 5, 6, 7, 8}. Define a relation R on A by aRb if and only if 3 divides a − b for all a, b ∈ A. Show that R is an equivalence relation on A. Find the equivalence classes [1], [2], [3], and [4].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let A = {1, 2, 3, 4, 5, 6, 7, 8}. Define a relation R on A by
aRb if and only if 3 divides a − b
for all a, b ∈ A. Show that R is an equivalence relation on A. Find the equivalence classes [1], [2],
[3], and [4].
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