The relation "has the same father as' over the set of children (a) only reflexive (b) only symmetric (c) only transitive (d) an equivalence relation

The relation has the same father as over the set of children is:

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

The relation less than in the set of natural numbers is (a) only symmetric (b) only transitive (c) only reflexive (d) 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

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

Let A={1, 2, 3) be a given set. Define a relation on A swhich is (i) reflexive and transitive but not symmetric on A (ii) reflexive and symmeetric but not transitive on A (iii) transitive and symmetric but not reflexive on A (iv) reflexive but neither symmetric nor transitive on A (v) symmetric but neither reflexive nor transitive on A (vi) transitive but neither reflexive nor symmetric on A (vii) neither reflexive nor symmetric and transitive on A (vii) an equivalence relation on A (ix) neither symmetric nor anti symmmetric on A (x) symmetric but not anti symmetric on A

Give an example of a relation which is reflexive and symmetric but not transitive.

Give an example of a relation which is reflexive and symmetric but not transitive.