Let No = (NU{0}) be the set of natural numbers including 0. Let M = N = (No x No × No): relation - on M x M is defined as I~y (a, b, c) ~ (d, e, f) = a +b+c=d+e+f a) Prove that ~ is an equivalence relation. b) Determine all elements of the equivalence class (1,0, 1). c) Let z = (a, b, c) E M and y = (d, e, f) E M. the relation < on M x M is defined as follows: %3D I< y (a, b, c) < (d, e, f) a
Let No = (NU{0}) be the set of natural numbers including 0. Let M = N = (No x No × No): relation - on M x M is defined as I~y (a, b, c) ~ (d, e, f) = a +b+c=d+e+f a) Prove that ~ is an equivalence relation. b) Determine all elements of the equivalence class (1,0, 1). c) Let z = (a, b, c) E M and y = (d, e, f) E M. the relation < on M x M is defined as follows: %3D I< y (a, b, c) < (d, e, f) a
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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