Question

6 Show that the relation Run 2 of integens given by : R=4 (214) id-y is divisible by 5; Ryen Zus an equivalence Welation:

11th - 12th Class

Maths

Solution

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as ( x-x=0 ) which is divisible by ( s ) R is rebuxive as ( x-y ) is sdivisible bys So ( y-x=-(x-y) ) is also divirible by 5 R is traustive [ begin{array}{l} x-y=a(s) y-z=b(s) g_{0} quad x-z=(x-y)+(y-z)=a(s)+b(s) =(a+b) s end{array} ] Q. So ( x-z ) is also divisible bys As ( R ) is seflexive , symmetnic and trancitive, ( R ) is equivalent