Let R be a relation from set Q to Q defined as:
`R={(a,b):a,b in Q and a -b in Z}`
Prove that
(i) For each `a in Q, (a,a) in R`
`(ii) (a,b) in R implies (b,c) in R` where `a, b in Q`
(iii) `(a,b) in R , (b,c) in R implies (a,c) in R ` , where `a, b ,c 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}. Showt ^(^^){a,a) in R for all a in Q,{a,b}in R rArr that {b,a}in R,{a,b}in R and {b,c}in R rArr t widehat a,c in R

Let R be the relation of the set Z of all integers defined by : R = {(a,b) : a, b in Z and (a-b) " is divisible by " n in N} Prove that : (i) (a,a) in R for all a in Z (ii) (a,b) in R rArr (b,a) in R for all a, b in Z (iii) (a,b) in R and (b,c) in R rArr (a,c) in R " for all" a,b,c in Z

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 R be a relation in N defined by R={(a , b); a , b in N\ a n d\ a=b^2dot} Are the following true: (i)\ (a , a) in R\ AA\ a in N (ii)\ (a , b) in R=>(b , a) in R (iii)\ (a , b) in R ,(b , c) in R=>(a , c) in R

A relation R in a set A is called ___ if (a,b) in R implies that (b,a) in R for all a,b in R

Let R be a relation over the set NxxN and it is defined by (a,b)R(c,d)impliesa+d=b+c . Then R is

If relation R_1={(a,b):a,b in R,a^2+b^2 in Q} and R_2={(a,b):a,b in R, a^2+b^2 !in Q} Then

Let R_(1) and R_(2) be two relation defined as follows : R_(1) = { (a,b) in R^(2) , a^(2) + b^(2) in Q} and R_(2) = {(a,b) in R^(2) , a^(2) + b^(2) cancel(in)Q) where Q is the set of the rational numbers. Then:

If p^(a)=q^(b)=r^(c)=s^(d) and p,q,r,s are in G.P then a,b,c,d are in