2. Let R(A,B,C) and S(A,B,C) be two relations, and no attributes can have null value.

Determine whether each of the following equations always holds in which R, S, and all

operations are interpreted to be sets and set-operations.

What if R, S, and all operations are bags and bag-operations? Please explain your answer

in detail. (20 pts)

a). (R INTERSECT S) = (R JOIN S)

b). (((R-S) UNION (S-R)) INTERSECT (R INTERSECT S)) = EMPTYSET

c). DELTA(R) = GAMMA_{A.B.C}(R)

d). (R UNION S) = R