Suppose that relation R$($A$,$ B$)$ has an instance r with n tuples and

S$($A$,$ C$)$ has an instance s with m tuples $($n$,$ m $>0).$

Fill out the following tables for the maximum and minimum possible number of tuples in each

relational algebra expression for each of the following three cases. $($a$)[6$ pts$]$ When $A$ is a key $($i$.$e$.,$ unique$)$ for $R.$

$($b$)[6$ pts$]$ When $A$ is a key for $R$ and $A$ is a foreign key for $S($referencing $R).$

$($c$)[6$ pts$]$ Without any condition for keys.