For each of the SQL aggregate functions sum, count, min and max, show how to compute the aggregate value on a multiset S1 ∪ S2, given the aggregate values on multisets S1 and S2.

Based on the above, give expressions to compute aggregate values with grouping on a subset S of the attributes of a relation r (A, B, C, D, E), given aggregate values for grouping on attributes T ⊇ S, for the following aggregate functions:

a. sum, count, min and max

b. avg

c. standard deviation