On the set Z of integers, relation R is defined as "`a R b hArr a+2b` is an integral multiple of 3". Which one of following statements is correct for R? (a) R is only reflexive (b) R is only symmetric (c) R is only transitive (d) R is an equivalence relation

Statement-1: On the set Z of all odd integers relation R defined by (a, b) in R iff a-b is even for all a, b in Z is an equivalence relation. Statement-2: If a relation R on a set A is symmetric and transitive, then it is reflexive and hence an equivalence relation, because (a, b) in Rimplies(b, a)in R" [By symmetry]" (a, b)in R and (b, a) in Rimplies (a,a)in R " [By transitivity]"

Statement-1: On the set Z of all odd integers relation R defined by (a, b) in R iff a-b is even for all a, b in Z is an equivalence relation. Statement-2: If a relation R on a set A is symmetric and transitive, then it is reflexive and hence an equivalence relation, because (a, b) in Rimplies(b, a)in R" [By symmetry]" (a, b)in R and (b, a) in Rimplies (a,a)in R " [By transitivity]"

If l is the set of integers and if the relation R is defined over l by aRb, iff a - b is an even integer, a,b inl , the relation R is: (a) reflexive (b) anti-symmetric (c) symmetric (d) equivalence

R is a relation on the set Z of integers and it is given by (x ,\ y) in RhArr|x-y|lt=1. Then, R is (a) reflexive and transitive (b) reflexive and symmetric (c) symmetric and transitive (d) an equivalence relation

R is a relation on the set Z of integers and it is given by (x ,\ y) in RhArr|x-y|lt=1. Then, R is (a) reflexive and transitive (b) reflexive and symmetric (c) symmetric and transitive (d) an equivalence relation

If R is the relation in N xx N defined by (a, b) R (c,d) if and only if (a + d) =(b + c), show that R is an equivalence relation.

Which of the following statements is not correct for the R by a Rb if and only if b lives within one kilometer from a (a) R is reflexive (b) R is symmetric (c) R is not anti-symmetric (d) None of the above

If R is an equivalence relation on a set A, then R^(-1) is A reflexive only B.symmetric but not transitive C.equivalence D.None of these

Show that the relation R is R defined as R = {(a,b) : a le b} is reflexive and transitive but not symmetric.

If R is a relation in N xx N , show that the relation R defined by (a, b) R (c, d) if and only if ad = bc is an equivalence relation.