Let S be the set of all rest numbers and lets
`R={(a,b):a,bin S and a=+-b}.`
Show that R is an equivalence relation on S.

Let R be a relation on the set Q of all rationals defined by R={(a,b):a,binQ" and "a-binZ}. Show that R is an equivalence relation.

A relation S is defined on the set of real numbers R R a follows: S={(x,y) : s,y in R R and and x= +-y} Show that S is an equivalence relation on R R .

Let S be a relation on the set R of all real numbers defined by S={(a ,\ b) in RxxR : a^2+b^2=1} . Prove that S is not an equivalence relation on R .

Let S be a relation on the set R of all real numbers defined by S={(a,b)epsilon RxR:a^(2)+b^(2)=1}. Prove that S is not an equivalence relation on R.

Let S be a relation on the set R of all real numbers defined by S={(a , b)R×R: a^2+b^2=1}dot Prove that S is not an equivalence relation on Rdot

Let S be the set of all real numbers. Then the relation R= {(a,b):1+abgt0} on S is

Let S be the set of all real numbers. Then the relation R= {(a,b):1+abgt0} on S is

Let S be a relation on the set R of all real numbers defined by S={(a , b)RxR: a^2+b^2=1}dot Prove that S is not an equivalence relation on Rdot

Let Z be the set of integers.Show that the relation R={(a,b):a,b in Z and a+b is even } is an equivalence relation on Z .