Question

Let R be the relation from A={2,3,4,5} to B={3,6,7,10} defined by ‘x divides y’,

(a) thenR^(-1) is equal to:

(b) Is R an equivalence relation?

Answer 1

We have $R=\{(2,6),(2,10),(3,3),(3,6),(5,10)\}$, then $R^{-1}=\{(6,2),(10,2),(3,3),(6,3),(10,5)\}$.

$R$ is not an equivalnce relation, because $A$ - domain of $R$ not equals $B$ - range of $R$.