Let be partitioned into the subsets B_1= 1,4,7 , B_2= 2,5,8 , B_3= 3,6,9

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

A=\{1,2,3,4,5,6,7,8,9\}

be partitioned into the subsets

B_1=\{1,4,7\},\quad B_2=\{2,5,8\},\quad B_3=\{3,6,9\}.

Using this partition, respond to the following: (i) Define the equivalence relation

R

A

that is induced by the given partition. (ii) Prove that, for any

x,y\in A

x\,R\,y

if and only if

x\equiv y \pmod{3}

. (iii) Write the full equivalence class that contains the element

5