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Functional Dependencies
Functional Dependencies Concept:
Let R be the relation X, Y are non – empty sets of attributes over R and are any tuple of R.
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Here X and Y may single or multiple attributes like
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Here X functionally determined Y or Y is functionally determined by X.
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| p | q | p ⇒ q |
Case 1 | 0 | 0 | 1 |
Case 2 | 0 | 1 | 1 |
Case 3 | 1 | 0 | 0 |
Case 4 | 1 | 1 | 1 |
Case 1:
R
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So,
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Case 2:
R
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So,
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Case 3:
R
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So,
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Case 4:
R
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So,
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Note: All cases are true except case 3, so to check functional dependency (F.Ds) we only check case 3 which tells us it is F.Ds or not.
We can say:
(Any key) → Any attributes
The reason is key is always unique never duplicate.
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So, Case 3 never possible
Student
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As we know Sid is a key attribute so, Sid → (Any attribute)
So, Case 3 never possible
How many F.Ds we can get from Sid:
Key Attribute → Any attribute
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Now check the following FDs
1. Cid → Cname: (case 3 not occurred) So, it is possible.
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2. Sname → Cid
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Here case 3 occurred. So, it is false.
3. Sname → Cname
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Case 3 occurred. So, it is false.
4. Sname → Sid
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Case 3 occurred. So, it is false.
5. Cid → Sid
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Case 3 occurred. So, it is false.
6. Cid → Sname
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Case 3 occurred. So, it is false.
7. Cname → Cid
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It is true, so, case 3 not possible.
