# Let us make the following gross simplifications regarding the number of tuples that appear in…

Let us make the following gross simplifications regarding the number of tuples that appear in relations that are the result of the operations of relational algebra.

i) Each operand relation has 1000 tuples.

ii) When we join relations with n and m tuples, respectively, the resulting relation has mn/100 tuples.

iii) When we perform a selection whose condition is the AND of k conditions, each of which equates an attribute to a constant value, we divide the size of the relation by 10k .

iv) When we perform a projection, the size of the relation does not change.

Further, let us estimate the cost of evaluating an expression by the sum of the sizes of the relations computed for each interior node. Give the costs of each of the expressions in Figs. 8.18, 8.19(a) through (d), and 8.20(a) through (d).

Fig. 8.18. Initial expression to determine where C. Brown is at 9AM, Mondays.

Fig. 8.19. Pushing the selection down.