The relation R on R defined as R={(a ,b) : `a <=b`} is an equivalence relation. State true or false.

The relation R in R defined as R={(a,b):a (A) Reflexive and symmetric (B) Transitive and symmetric (C) Equivalence (D) Reflexive,transitive but not symmetric

Show that the relation R in R defined as R={(a,b):ageb} is transitive.

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

Check whether the relation R on R defined by R={(a,b):a<=b^(3)} is reflexive,symmetric or transitive.

Check whether the relation R in R defined by R={(a,b):a<=b^(3)} is reflexive,symmetric or transitive.

Let R be a relation on Z defined by : R = {(a,b) : a in Z , b in Z, a^(2) = b^(2)} . Then range of R = _____.

Let Z be the set of all integers and R be the relation on Z defined as R={(a,b);a,b in Z, and (a-b) is divisible by 5.}. Prove that R is an equivalence relation.