1) Suppose relation R(A,B,C) has the tuples:

A	B	C
1	2	3
1	2	3
2	3	1
3	1	2
2	2	3
2	3	3

Using bag projection and intersection, compute PROJ_A,B(R) INTERSECT RENAME_S(A,B)(PROJ_B,C(R)). Note that the renaming is only to give the two projections the same schema.

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