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.

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.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

Let R be a relation on the set A of ordered pairs of integers defined by (x,y)R(u,v) iff xv=yu .Show that R is an equivalence relation.

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

Show that the relation R in the set of all integers, Z defined by R = {(a, b) : 2 "divides" a - b} is an equivalence relation.

Let R be a relation from Q to Q defined by R={(a,b): a,b in Q and a-b in Z} . Show that (i) (a,a) in R" for all " a in Q

Let R be a relation from Q to Q defined by R={(a,b): a,b in Q and a-b in Z} . Show that (i) (a,a) in R" for all " a in Q

Let R be a relation from Q to Q defined by : R = {(a, b): a,b in Q and a-b in Z }. Show that : (a, a) in R for all a in Q.

Let R be the relation on Z defined by aRb iff a-b is an even integer. Show that R is an equivalence relation.