Let W(A, B) and Q(C,D) be two relation schemas. Let r₁ and r2 be the corresponding relation instances. B is a foreign key that refers to C in r2. Assuming that all tuples in r₁ and r2 satisfy referential integrity constraints, which of the following is ALWAYS TRUE? (А) Пв (1) - Пс (rz) =Ø (В) Пс (г) - Пв (г1 ) =Ø (С) Пв (г1) = Пс (12) (D) IIB (1₁) - IIc (1₂) *Ø B A

Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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**Problem Statement:**

Let \( W(A, B) \) and \( Q(C, D) \) be two relation schemas. Let \( r_1 \) and \( r_2 \) be the corresponding relation instances. \( B \) is a foreign key that refers to \( C \) in \( r_2 \). Assuming that all tuples in \( r_1 \) and \( r_2 \) satisfy referential integrity constraints, which of the following is ALWAYS TRUE?

**Options:**

- **(A)** \( \Pi_B (r_1) - \Pi_C (r_2) = \emptyset \)
- **(B)** \( \Pi_C (r_2) - \Pi_B (r_1) = \emptyset \)
- **(C)** \( \Pi_B (r_1) = \Pi_C (r_2) \)
- **(D)** \( \Pi_B (r_1) - \Pi_C (r_2) \neq \emptyset \)

**Explanation:**

In this problem, referential integrity implies that every value of \( B \) in \( r_1 \) must have a corresponding value of \( C \) in \( r_2 \). Therefore, the correct answer is always aligning with this rule.

With this integrity constraint, the choice that will always hold true is:

**Option (A)**: \( \Pi_B (r_1) - \Pi_C (r_2) = \emptyset \).

This means that there are no elements in \( \Pi_B (r_1) \) (projection of attribute \( B \) from \( r_1 \)) that are not also in \( \Pi_C (r_2) \) (projection of attribute \( C \) from \( r_2 \)) – satisfying the referential integrity condition.
Transcribed Image Text:**Problem Statement:** Let \( W(A, B) \) and \( Q(C, D) \) be two relation schemas. Let \( r_1 \) and \( r_2 \) be the corresponding relation instances. \( B \) is a foreign key that refers to \( C \) in \( r_2 \). Assuming that all tuples in \( r_1 \) and \( r_2 \) satisfy referential integrity constraints, which of the following is ALWAYS TRUE? **Options:** - **(A)** \( \Pi_B (r_1) - \Pi_C (r_2) = \emptyset \) - **(B)** \( \Pi_C (r_2) - \Pi_B (r_1) = \emptyset \) - **(C)** \( \Pi_B (r_1) = \Pi_C (r_2) \) - **(D)** \( \Pi_B (r_1) - \Pi_C (r_2) \neq \emptyset \) **Explanation:** In this problem, referential integrity implies that every value of \( B \) in \( r_1 \) must have a corresponding value of \( C \) in \( r_2 \). Therefore, the correct answer is always aligning with this rule. With this integrity constraint, the choice that will always hold true is: **Option (A)**: \( \Pi_B (r_1) - \Pi_C (r_2) = \emptyset \). This means that there are no elements in \( \Pi_B (r_1) \) (projection of attribute \( B \) from \( r_1 \)) that are not also in \( \Pi_C (r_2) \) (projection of attribute \( C \) from \( r_2 \)) – satisfying the referential integrity condition.
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