The relation R on integers given by x R y iff x2 y2 give th

The relation R on integers given by x R y iff x^2 = y^2. give the equivalence class of 0; of 4; of -72

Solution

Equivalence class of a is denoted by [ a ] and is defined by

[ a ] = { b Z | bRa iff b² = a² }

Then [ 0 ] = { 0 }   since 0R0 iff 0² = 0²

        [ 4 ] = { - 4 , 4 } since ( - 4 )R( 4 ) iff ( - 4 )² = ( 4 )²

and   [ - 72 ] = { - 72 , 72 }   since ( - 72 )R( 72 ) iff ( - 72 )² = ( 72 )²