Database Management Systems - Relational Algebra quiz

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Let us use the following relations R and S to answer the questions 1 – 10s;
A B 3 3 6 4 2 3 3 5 3 6	B C D 5 1 6 3 3 5 4 3 1
1. Compute R ⋈ S. Which of the following records will be in the result? Assume each record has the schema (A, B, C, D).
(a) (3, 3, 1, 6)	(b) (6, 4, 4, 1)
(c) (2, 3, 3, 5)	(d) (3, 5, 3, 1)
2. Compute R ⋈R.A<S.C S. [this is theta join]. Which of the following records will be in the result? Assume each record has the schema (A, B, C, D).
(a) (2, 3, 3, 5)	(b) (6, 4, 4, 1)
(c) (6, 4, 3, 1)	(d) (3, 5, 1, 6)
3. Compute R ⋈R.B < S.D AND R.A<S.C S. [this is theta join]. Which of the following records will be in the result? Assume each record has the schema (A, B, C, D).
(a) (3, 3, 3, 5)	(b) (6, 4, 3, 1)
(c) (2, 3, 3, 5)	(d) (3, 5, 1, 6)
4. Compute π C, D (S). Which of the following records will be in the result?
(a) (5, 1)	(b) (4, 3)
(c) (3, 3)	(d) (3, 5)
5. Compute π B, C (R ⋈ S). Which of the following records will be in the result?
(a) (6, 4)	(b) (4, 3)
(c) (5, 1)	(d) (5, 3)
6. Compute π B (R) - π B (S). Which of the following records will be in the result?
(a) (6)	(b) (4)
(c) (1)	(d) (5)
7. Compute π B (R) ∩ π B (S). Which of the following records will be in the result?
(a) (6)	(b) (1)
(c) (2)	(d) (5)
8. Compute R ⋈ S. Which of the following records will be in the result? Assume each record has the schema (A, B, C, D).
(a) (3, 3, 1, 6)	(b) (6, 4, 4, 1)
(c) (3, 5, 1, 6)	(d) (3, 5, 3, 1)
9. Compute π B (R) U π B (S). Which of the following records will be in the result?
(a) (6)	(b) (1)
(c) (2)	(d) (5)
10. Assume a relation R(A, B) with n unique records, and a relation S(B, C) with m unique records. When you compute the natural join between R and S you shall get r records as the result. Which of the following assumptions are correct in terms of (n, m, r)?
(a) (5, 4, 25)	(b) (2, 3, 8)
(c) (3, 3, 10)	(d) (2, 3, 6)

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