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`
(ii) `(a,b) in R` implies that `(b,a) inR `
(iii) `(a,b) in R and (b,c) in R` implies that `(a,c) in R`

Let R be a relation from N to N defined by R={(a,b): a, b in N and a=b^(2)}. Are the following true? (i) (a,a) in R," for all " a in N (ii) (a,b) in R," implies "(b,a) in R (iii) (a,b) in R, (b,c) in R" implies "(a,c) in R . Justify your answer in each case.

Let R:ZrarrZ be a relation defined by R = {(a,b):a,b,inZ, a -b in z) . Show that (i) AAa inZ, (a,a) inR (ii) (a,b) inR implies (b,a)inR (iii) (a,b) inR implies (b,c)inRimplies(a,c)inR

Let R be the relation on Z defined by R= {(a,b): a, b in Z, a-b is an integer}. Find the domain and range of R.

Let R be a relation defined by R = {(a, b) : a ge b }, where a and b are real numbers, then R is

Let R be the relation in the set N given by R={(a,b), a=b -2, b gt 6}. Choose the correct answer.

Let A = {1, 2, 3} and R = {(a,b): a,b in A, a divides b and b divides a}. Show that R is an identity relation on A.

Let R be the relation over the set N xx N and is defined by (a,b)R(c,d) implies a+d=b+c . Then R is :

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

Let R be the equivalence relation on z defined by R = {(a,b):2 "divides" a - b} . Write the equivalence class [0].

Let R be a relation on the set Z of all integers defined by:(x,y) in R implies(x-y) is divisible by n.Prove that (b) (x,y) in R implies(y,x) in R for all x,y,z in Z .