The minimum number of tuples in $R$ Natural join $S$ is $zero,$ when both relations have a common attribute, but does not satisfy the condition.
Let us say
$R$
$S$
$R\Join_{<b=b>} S$
Number of tuples $=0$
And if both relation does not have any common attribute then natural join works as a cartessian product(or cross product).
$R$
$S$
$R$ Natural Join $S$
a |
b |
c |
d |
1 |
2 |
4 |
5 |
1 |
2 |
6 |
7 |
2 |
3 |
4 |
5 |
2 |
3 |
6 |
7 |
Number of tuples $=4$