This is the statement that I need to prove:
Let R and S be two relations on set U, of which R is transitive and S is reflexive. Prove that: (R;S;R)^3 is a subset of (R;S)^3.
The obvious way to prove this is to: assume some x that is the element of (R;S;R)^2 and prove that it is also element of (R;S)^3. However, I have no idea how to do this, or how to use the properties of transitivity and reflexivity to do it.
Any help is greatly appreciated. Thank you in advance!
Cheers :)