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 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 a relation on N xx N defined by (a,b) R(c, d) hArr a + d= b + c for all (a,b) (c,d) in N xx N show that, (a, b) R (a,b) for all (a, b) in N xx N

Let R be the relation on 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 a relation on N xx N defined by (a,b) R(c, d) hArr a + d= b + c for all (a,b) (c,d) in N xx N show that, (a,b) R (c, d) rArr (c, d) R (a, b) for all (a, b) (c, d) in N xx N

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

** be a binary operation on R defined by a"*"b = (a)/(4)+b/(7) , a,b inR . Show that ** is not commutative and associative.