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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

1. $m+n$ and $0$
2. $mn$ and $0$
3. $m+n$ and $|m-n|$
4. $mn$ and $m+n$
edited | 5k views
–4
ans plz

$mn$
Case 1: if there is a common attribute between $R$ and $S$, and every row of $r$ matches with the each row of $s$- i.e., it means, the join attribute has the same value in all the rows of both $r$ and $s$,
Case 2: If there is no common attribute between $R$ and $S.$

$0$ There is a common attribute between $R$ and $S$ and nothing matches- the join attribute in $r$ and $s$ have no common value.

edited
+7
mn occurs during cartesian product of two relation ....

and 0 occurs during natural join of two realtion(In best case )....
+20
^
Join means Natural Join only.
Natural Join gives result as cartesian product if no attribute is matching in both relations.
eg- $R(A,B)$ and $S(C,D)$

Natural Join gives result as empty relation  if  at least one of the attribute matches but value does not matches.
$\begin{tabular}{ |c|c| } \hline \multicolumn{2}{|c|}{R} \\ \hline A & B \\ \hline a1 & b1 \\ a2 & b2 \\ a3 & b3 \\ \hline \end{tabular}$

$\begin{tabular}{ |c|c| } \hline \multicolumn{2}{|c|}{S} \\ \hline B & C \\ \hline b3 & c1 \\ b4 & c2 \\ b5 & c3 \\ \hline \end{tabular}$

In this case $R \Join S$ is empty.
0
Thanks @Sachin it  more clear now.