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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 | 5.4k 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
+8
mn occurs during cartesian product of two relation ....

and 0 occurs during natural join of two realtion(In best case )....
+32

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.

In this case $R \Join S$ is empty.

0
Thanks @Sachin it  more clear now.
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sachin sir shukriya
0

Join means Natural Join only.

in sql, it is ok... but in Relational Algebra, as per my knowledge, we can't say join means  Natural join

0
why in the above example R$\infty$S is { R JOIN S} IS EMPTY??

it should return  a3 b3 c1

isnt it??
0

@Shaik Masthan

can u pls give an example in which maximum size of join is m*n; i am getting size of join as max(m,n)

+1

why in the above example R∞S is { R JOIN S} IS EMPTY??

actually, there is a typo in previous image, corrected now !

can u pls give an example in which maximum size of join is m*n;

when no common attributes are there in the relations, then it is equivalent to cartesian product ==> m*n possible

0
is there any specific logic/ trick to how to find total no. of tuples when there is a common attribute!

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