Relations: How to prove $R^2R^3 = R^5$ ?
I tried to go by this definition but I'm not quite sure I'm in the right path.
$RS = \{(x,y) | \exists z, (x,z) \in R$ ^ $(z,y) \in S\}$
Relations: How to prove $R^2R^3 = R^5$ ?
I tried to go by this definition but I'm not quite sure I'm in the right path.
$RS = \{(x,y) | \exists z, (x,z) \in R$ ^ $(z,y) \in S\}$
$$R^2R^3=(R R)(R R R)=R R R R R=R^5$$