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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