Changes between Initial Version and Version 1 of Proof of 3N

Timestamp:

01/28/26 00:05:05 (13 days ago)

Author:

213087

Comment:

--

Proof of 3N

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+=== Third Normal Form (3NF) – Detailed Explanation ===
+
+Third Normal Form builds on Second Normal Form by eliminating transitive dependencies.
+
+
+Even though 2NF removes partial dependencies, data anomalies can still exist if non-key attributes depend on other non-key attributes.
+
+=== Formal Definition of 3NF ===
+
+A relation R is in Third Normal Form (3NF) if and only if:
+
+**R is already in Second Normal Form (2NF)**
+
+**For every functional dependency X → A, at least one of the following holds:
+
+1.X is a superkey, OR
+
+2.A is a prime attribute (part of some candidate key)
+
+This definition ensures that non-key attributes depend only on the primary key and nothing else.**
+
+=== Why 3NF Is Necessary in Wedding Planner ===
+
+In the Wedding Planner system, many entities are logically independent, but still connected:
+
+1.Weddings are created by users
+
+2.Venues have descriptive properties
+
+3.Bookings connect weddings and venues
+
+If descriptive attributes are stored indirectly via other non-key attributes, transitive dependencies arise, which violate 3NF.
+
+=== Relations After 2NF (Starting Point for 3NF) ===
+
+|| Table || Primary Key || Attributes ||
+|| user || user_id || user_first_name, user_last_name, user_email 
+|| wedding || wedding_id || wedding_date, wedding_budget, user_id 
+|| venue || venue_id || venue_name, venue_type, venue_capacity 
+|| venue_booking || booking_id || venue_id, wedding_id, booking_date, start_time, end_time ||
+
+All relations are in 2NF, but this does not guarantee 3NF.
+
+=== Identification of Transitive Dependencies ===
+
+A transitive dependency exists when:
+
+**Primary Key → Non-Key Attribute → Another Non-Key Attribute**
+
+=== Transitive Dependency Analysis ===
+
+|| Dependency Chain || Explanation ||
+|| wedding_id → user_id → user_email || wedding_id indirectly determines user data 
+|| booking_id → venue_id → venue_name || booking_id indirectly determines venue attributes ||
+
+In both cases:
+
+**1.The middle attribute (user_id, venue_id) is not a key
+
+2.The final attribute is non-key
+
+3This violates 3NF**
+
+=== Why This Violates 3NF (Formal Proof) ===
+
+Consider:
+
+wedding_id → user_id
+user_id → user_email
+
+By transitivity:
+
+wedding_id → user_email
+
+Since:
+
+wedding_id is not a superkey of the user relation
+
+user_email is not a prime attribute
+
+➡ 3NF is violated
+
+=== Decomposition Strategy for 3NF ===
+
+To eliminate transitive dependencies:
+
+*Each non-key attribute must depend directly on the primary key
+
+*Intermediate determining attributes must be separated into their own relations
+
+*This process does not lose data and does not break dependencies.
+
+=== 3NF Decomposition (Final Relations) ===
+
+=== USER ===
+
+|| user_id || user_first_name || user_last_name || user_email ||
+|| 1 || Ana || Trajkovska || ana.trajkovska@gmail.com||
+
+FD:
+user_id → user_first_name, user_last_name, user_email
+
+=== WEDDING ===
+
+|| wedding_id || wedding_date || wedding_budget || user_id ||
+|| W01 || 2026-06-20 || 8500 || 1 ||
+
+FD:
+wedding_id → wedding_date, wedding_budget, user_id
+
+=== VENUE ===
+
+|| venue_id || venue_name || venue_type || venue_capacity ||
+|| W011 || Lakeside Garden Venue || Outdoor Garden || 200 ||
+
+FD:
+venue_id → venue_name, venue_type, venue_capacity
+
+=== VENUE_BOOKING ===
+
+|| booking_id || venue_id || wedding_id || booking_date || start_time || end_time ||
+|| B01 || V01 || W01 || 2026-06-20 || 12:00 || 13:00 ||
+
+FD:
+booking_id → venue_id, wedding_id, booking_date, start_time, end_time
+
+=== Proof That 3NF Conditions Are Satisfied ===
+
+For every functional dependency:
+
+|| Dependency || Determinant Type ||
+|| user_id → user_email || user_id is PK 
+|| wedding_id → wedding_budget || wedding_id is PK 
+|| venue_id → venue_type || venue_id is PK 
+|| booking_id → start_time || booking_id is PK ||
+
+**✔ All determinants are superkeys**
+
+**✔ No non-key attribute determines another non-key attribute**