7.Define a relation p on N × N by (a, b)p(c, d) if and only if there is ad = bc.(a) Show that p is an equivalence relation.(b) As always, we use [(2, 3)] to mean the equivalence class of (2, 3). Determine if (1,2) = [(2,3)],(4,6) = [(2,3)] and (10,15) = [(2,3)].

Part (a): Proving that ρ is an equivalence relationAn equivalence relation must satisfy three…

Answered: 7. Define a relation p on N × N by (a,…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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7. Define a relation p on N × N by (a, b)p(c, d) if and only if there is ad = bc. (a) Show that p is an equivalence relation. (b) As always, we use [(2, 3)] to mean the equivalence class of (2, 3). Determine if (1,2) = [(2,3)], (4,6) = [(2,3)] and (10,15) = [(2,3)].