Relational Algebra & Bag Semantics

R                   S 
-------------       ---------
| A | B | C |       | C | D |
-------------       ---------
| 1 | 1 | 2 |       | 4 | 2 |
| 1 | 1 | 2 |       | 4 | 2 |
| 1 | 2 | 3 |       | 2 | 1 |
| 1 | 2 | 3 |       | 2 | 1 |
| 1 | 2 | 3 |       | 2 | 6 |
| 1 | 4 | 1 |       | 3 | 2 |
| 1 | 5 | 1 |       ---------
-------------

Consider the relations R and S shown above. Let π^*, σ^*, ∩^*, ∪^*, −^*, ×^* denote the bag semantic versions of the relational algebra (RA) operators. Computer the results of the following queries.

1. ( π_C(R)) ∪ (π_C(S))

2. ( π^*_C(R)) ∪^* (π^*_C(S))

3. δ ( π^*_C(R) )

4. γ_{B,C,Count(B,C) → E} R

5. τ_D(S)

6. π^*_{A → F, B²+C → G} (R)

7. R ⋈^*_L S

8. R ⋈^*_R S