Dbms, relational algebra.

Question

Consider two relations R1 , R2 with N1 and N2 tuples where N2 > N1 > 0, what are the minimum and maximum rows for the RA expression R2/R1  ?

Comments

The expression for number of tuples in $\frac{R2}{R1} $ will be $\frac{N2}{N1}$.

The minimum value of this will be 1 , and maximum will be $N2$.

This can be checked by taking examples.

For the minimum case , let's take this example.

R2 has two tuples :-

a 1

a 2

and R1 has only one tuple :-

1.

Thus o/p of R2/R1 will be only 'a' as a single tuple.

 

For maximum case,

R2 has 3 tuples  :-

a 1

b 1

c 1

And R1 has single tuple:-

1.

so the o/p of R2/R1 will be :-

a

b

c.

Thus this is the max case.

Answer 1

minimum :-0

maximum:-floor(n2/n1).

Answer 2

• The expression for MINIMUM NUMBER OF number of tuples in R1/R2 will be 0.
• The expression for maximum  number of tuples in R1/R2 will be N1/N2.