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Let R be a relation on NxxN defined by (...

Let `R` be a relation on `NxxN` defined by `(a , b)\ R(c , d)hArra+d=b+c\ for\ a l l\ (a , b),(c , d) in NxxN` show that: `(i)\ (a , b)R\ (a , b)\ for\ a l l\ (a , b) in NxxN` `(ii)\ (a , b)R(c , d)=>(c , d)R(a , b)for\ a l l\ (a , b),\ (c , d) in NxxN` `(iii)\ (a , b)R\ (c , d)a n d\ (c , d)R(e ,f)=>(a , b)R(e ,f)\ ` for all`\ (a , b),\ (c , d),\ (e ,f) in NxxN`

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(i) If (a,b)R(c,d) then (c,d)R(a,b) as if a+d=b+c then b+d=a+c . Thus relation R is symmetric .`\ (a , b)R\ (a , b)\ for\ a l l\ (a , b) in NxxN`

(ii)`\ (a , b)R(c , d)=>(c , d)R(a , b)for\ a l l\ (a , b),\ (c , d) in NxxN`For some a,b in N , (a,b)R(a,b) as a+b=b+a. Thus every element of N×N is related to itself, So relation R is also reflexive .

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