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 12E: Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and...

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Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.
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ii. Determine whether the relation, R = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} is: Yes/No Justify your answer. Types of relations Reflexive Symmetric Antisymmetric Transitive (8 marks)
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Let x1, x2, y1, y2 be real numbers. The expression (x1, y1) ~ (x2, y2) means that x12 + y12 = x22 + y22. Prove that the relation ~ is an equivalence relation on R2.
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R={(0,4), (3,0), (3,1), (4,2)}. Find transitive closer of R. Show diagram. A=Z+ x Z+ show relation R on A as for any (a,b) and (c,d), (a,b)R(c,d) (ab)=(cd) Show if R equ relation and explain List 4 elements in the equ class [(3,1)] Show distinct equ classes for R

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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)].