(d) If A → C and B → C and ABC → D, then A → D 数据库
时间: 2024-06-07 22:08:34 浏览: 11
According to the given functional dependencies, we can infer that:
- A uniquely determines C (A → C)
- B uniquely determines C (B → C)
- The combination of A, B, and C uniquely determines D (ABC → D)
Using these three functional dependencies, we can apply the transitive rule to infer that:
- A and B together uniquely determine C (A, B → C)
- A, B, and C together uniquely determine D (A, B, C → D)
Therefore, we can conclude that A, B, and C collectively determine D, and we can express this as:
A, B, C → D
相关问题
Prove If A → C and B → C and ABC → D, then A → D 数据库
To prove that A → D, we need to show that if A is true, then D must also be true.
Given that ABC → D, we know that if A and B and C are all true, then D must also be true.
We are also given that A → C and B → C, which means that if A is true, then C must also be true, and if B is true, then C must also be true.
Combining these two statements, if A is true, then B is also true (because if A were false, then we wouldn't have enough information to determine whether B is true or false). Therefore, if A and B and C are all true, then D must also be true (because of the ABC → D statement).
Therefore, we can conclude that A → D.
Prove If A → C and B → C and ABC → D, then A → D
To prove that A → D, we need to show that if A is true, then D must also be true.
We know that ABC → D, which means that if A, B, and C are all true, then D must also be true. Since A → C and B → C, we know that if A and B are true, then C must also be true.
Therefore, if A and B are true, then C is true, and if C is true, then D is true. So, if A is true, then D must also be true, and we have proved that A → D.
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