relation algebra

Question

Consider a relation R(A, B) that contains r tuples, and a relation S(B, C) that contains s tuples; assume r > 0 and s > 0. Make no assumptions about keys. For the following relational algebra expression, in terms of r and s the minimum and maximum number of tuples that could be in the result?

Comments

$r$ max

$0$ min

Answer 1

case 1: if in R(a,b) and S(b,c) we have the same values of b then the inner parenthesis evaluates to 0 and then r-0=r(no of tuples in relation r)

case 2: if in R(a,b) and S(b,c) we have no tuple common so the inner bracket gives us r no of tuples and r-r=0

So max=r and min=0