Assume that R and S are relations containing n R and n S tuples, respectively. What is the maximum and minimum number of tuples that can possibly be in the result of each of the following expressions (assuming appropriate union compatibilities)?
a. R ? S
b. R ? S
c. R ? S
d. R × S
e. R S
f. R / S
g. ?s=4(R) × ?s,t(S)
a. Maximum number of tuples: (nR + nS);
Minimum number of tuples: max(nR, nS).
b. Maximum number of tuples: min(nR, nS);
Minimum number of tuples: 0.
c. Maximum number of tuples: nR;
Minimum number of tuples: 0.
d. Maximum number of tuples: nR x nS;
Minimum number of tuples: nR x nS.
e. Maximum number of tuples: nR x nS;
Minimum number of tuples: 0.
f. Maximum number of tuples: nR / nS;
Minimum number of tuples: 0.
g. Maximum number of tuples: nR x nS;
Minimum number of tuples: 0. (Selection can be empty.)
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