Let R and S be two relations with the following schema R (P, Q, R1, R2, R3) S(P, Q, S1, S2) Where {P, Q} is the key for both schemas. Which of the following queries are equivalent?

I. $\Pi_P \left(R \bowtie S\right)$ II. $\Pi_P \left(R\right) \bowtie \Pi_P\left(S\right)$ III. $\Pi_P \left(\Pi_{P, Q} \left(R\right) \cap \Pi_{P,Q} \left(S\right) \right)$ IV. $\Pi_P \left(\Pi_{P, Q} \left(R\right) - \left(\Pi_{P,Q} \left(R\right) - \Pi_{P,Q} \left(S\right)\right)\right)$