Suppose there are three relational R(a,id), S(b,id), and T(c,id), each with r, s

Question

Suppose there are three relational R(a,id), S(b,id), and T(c,id), each with r, s, and t number of tuples and identical schema. Further r > s > t.

In terms of r, s, and t state the maximum and minimum number of tuples in the following expressions. Assume R,S,T to be sets with no nulls. Which answers will differ if R,S,T were bags.

a.(select * from R Union Select * from S) Union (select * from T)

b.(select * from R Intersect Select * from S) Intersect (select * from T)

c.(select * from R Union (select * from S Intersect select * from T)

d. (select * from R, S, T where R.id = S.id and S.id = T.id)

Explanation / Answer

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a)
Maximum number of tuples are r+s+t
Minimum number of tuples are r

b)
Maximum number of tuples are t
Minimum number of tuples are 0 or NULL

c)
Maximum number of tuples are r+t
Minimum number of tuples are r

d)
Maximum number of tuples are r*s*t
Minimum number of tuples are 0

d answer will differ if R,S,T were bags.

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