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`

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

if A relation R in a set A is called ………… if (a _(1), a _(2)) in R implies (a _(2) , a _(1)) in R for all a _(1) , a _(2) in A.

Let a relation R_(1) on the set R of real numbers be defined as (a,b)in R hArr1+ab>0 for all a,b in R .Show that R_(1) is reflexive and symmetric but not transitive.

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 a relation R_(1) on the set R of real numbers be defined as (a,b)in R_(11)+ab>0 for all a,b in R. show that R_(1) is reflexive and symmetric but not transitive.

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}. 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

If R be a relation in a set A and (x, y) in R rArr(y, x) in R AA x, y in A then the relation R is called (A) reflexive (B) symmetric (C) transitive (D) equivalence

The relation R, in the set of real number defined as R = {(a,b): a lt b} is: