VIPSolutionsIN STEP 1 GIVE THE INTRODUCTION OF THE CONCEPT AND GIVE ANSWER FOR EACH PART OF THE QUESTION IN EACH DIFFERENT STEP WITH CLEAR EXPLANATION AND IN THE FINAL STEP GIVE THE WHOLE FINAL ANSWER IN JUST VERY FEW SENTENCES AND MOREOVER I NEED COMPLETE AND CLEAR ANSWER at last explain what we did in each step in just few sentencesAE Nn ii iE a i fi it Hn LR i HH {hl HH hk i AR Ry HH i i Hh i ih i i ii ii i which orn HAY AR RA li GIES e following Function HR fl hh Hi oY nctional HRY A hs ol iH ed Yo AO Le i he a FRALEY d. — i NNN He vz Ro IH ih i yo FREY £ = li i I (i fi Hi il = — Hi 8% i i I I I Ih HAA 8 EL I We HH LL Hit lil hh § | i i il ae HE I Ln Lh lil ii — = | i. i | 0 Ti A = i Te ld — \ HA | I lh hi (= len He ji Hy — Ja Wn hl hl = HH =
Question:
IN STEP 1 GIVE THE INTRODUCTION OF THE CONCEPT AND GIVE ANSWER FOR EACH PART OF THE QUESTION IN EACH DIFFERENT STEP WITH CLEAR EXPLANATION AND IN THE FINAL STEP GIVE THE WHOLE FINAL ANSWER IN JUST VERY FEW SENTENCES AND MOREOVER I NEED COMPLETE AND CLEAR ANSWER at last explain what we did in each step in just few sentences
AE
Nn ii iE a
i fi it Hn LR i
HH {hl HH hk i AR Ry
HH i i Hh i ih i i ii ii i
which orn HAY AR RA li
GIES e following Function HR fl hh
Hi oY nctional HRY A hs ol
iH ed Yo AO Le i he a
FRALEY d. — i NNN
He vz Ro IH ih i yo
FREY £ = li i I (i fi Hi il = —
Hi 8% i i I I I Ih HAA 8
EL I We
HH LL Hit lil hh §
| i i il ae
HE I Ln Lh lil ii — =
| i. i | 0 Ti A =
i Te ld —
\ HA | I lh hi (=
len He ji Hy —
Ja Wn hl hl =
HH =
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Asked by: Test User 100221
Created at: 2025-05-10 07:19:24
Asked by: Test User 100221
Created at: 2025-05-10 07:19:24
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**Step 1: Introduction to the Concept of Functional Dependencies**
A **functional dependency** in a relation means that if two tuples (rows) agree on the value of some attribute(s) (the left side), they must also agree on the value of other attribute(s) (the right side). For example, if `X → Y` holds, whenever two rows have the same value for `X`, they must also have the same value for `Y`. We will check each dependency against the given table.
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**Step 2: Check Each Functional Dependency**
**a. X → Y**
- Check if rows with same X also have same Y.
- Rows 1 and 2: X=m and X=n (different, skip)
- Rows 3 and 5: X=o, Y=30 (all same)
- Rows 2 and 4: X=n, Y=30 (all same)
- No two rows with same X have different Y.
- **Conclusion:** X → Y **holds**.
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**b. Z → Y**
- Check if rows with same Z also have same Y.
- Rows 1, 3, 4, 5: Z=T, Y=20, 30, 30, 20 (Y differs for same Z)
- **Conclusion:** Z → Y **does NOT hold**.
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**c. Y → Z**
- Check if rows with same Y also have same Z.
- Rows 3, 4: Y=30, Z=T (same)
- Rows 1, 5: Y=20, Z=T (same)
- Row 2: Y=10, Z=F (only one instance)
- **Conclusion:** Y → Z **holds**.
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**d. XY → Z**
- Check if rows with same X and Y also have same Z.
- Each (X,Y) pair is unique except (o,30) in rows 3 and 5, both have Z=T.
- **Conclusion:** XY → Z **holds**.
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**e. YZ → X**
- Check if rows with same Y and Z also have same X.
- (Y=20, Z=T): Rows 1 and 5, X=m, X=o (different)
- **Conclusion:** YZ → X **does NOT hold**.
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**f. XZ → Y**
- Check if rows with same X and Z also have same Y.
- (o,T): Rows 3 and 5, Y=30 (same)
- (m,T): Row 1, Y=20 (only one instance)
- (n,T): Row 4, Y=30 (only one instance)
- (m,F): Row 2, Y=10 (only one instance)
- **Conclusion:** XZ → Y **holds**.
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**Step 3: Final Answer (Short Summary)**
The functional dependencies that hold in relation S are:
**a. X → Y, c. Y → Z, d. XY → Z, f. XZ → Y.**
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**Step 4: Explanation of Each Step**
- **Step 1:** Introduced what functional dependencies are.
- **Step 2:** Checked each dependency against the table by comparing relevant rows.
- **Step 3:** Summarized which dependencies hold in a concise answer.
- **Step 4:** Explained the process for clarity.
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