[" 13.Let "R" be a relation on "Q" defined by "],[" Prove that: "],[" (1) "(a,a)in R" for all "a in Q],[" (2) "(a,b)in R rArr(b,a)in R],[" (3) "(a,b)in R" and "(b,c)in R rArr(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 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 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 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 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 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 i) (a, a) in R for all a in Q ii) (a, b) in R implies that (b, a) in R iii) (a, b) in R and (b, c) in R implies that (a, c) in R .

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 , {a,b} in R implies that {b,a} in R, {a,b} in R and {b,c} in R implies that {a,c} in R

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, b) in R implies that (b, a) in R.