Consider the join of a relation R with a relation S. If R has m tuples and S has n tuples then the maximum and minimum sizes of the join respectively are

The relational algebra expression equivalent to the following tuple calculus expression:

$$\left\{ {t|t \in r \wedge \left( {t\left[ A \right] = 10 \wedge t\left[ B \right] = 20} \right)} \right\}$$ is:

Give a relational algebra expression using only the minimum number of operators from $$\left( { \cup ,\, - } \right)$$ which is equivalent to $$R \cap S$$.

An instance of a relational scheme R(A, B, C) has distinct values for attribute A. Can you conclude that A is a candidate key for R?