Let A = {1,2,3,4} x {1,2,3,4}, and define a relation R on A by (x1, y1)R(x2,y2) if x1 + y1 = x2 + y2. a. Verify that R is an equivalence relation on A. b. Determine the equivalence classes [(1,3)] , [(2,4)], and [(1,1)].

Let A = {1,2,3,4} x {1,2,3,4}, and define a relation R on A by (x1, y1)R(x2,y2) if x1 + y1 = x2 + y2. a. Verify that R is an equivalence relation on A. b. Determine the equivalence classes [(1,3)] , [(2,4)], and [(1,1)].

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} x {1,2,3,4}, and define a relation R on A by (x₁, y₁)R(x₂,y₂) if x₁+ y₁ = x₂ + y₂.

a. Verify that R is an equivalence relation on A.

b. Determine the equivalence classes [(1,3)] , [(2,4)], and [(1,1)].

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