=== Step 0: Initial Unnormalized Relation (UNF) ===

The system initially stores all information in a single relation:

USER_WEDDING_VENUE(user_id, user_first_name, user_last_name, user_email, wedding_id, wedding_date, wedding_budget, venue_id, venue_name, venue_type, venue_capacity, booking_id, booking_date, start_time, end_time)

This relation contains attributes describing multiple entities (User, Wedding, Venue, Booking).
Storing all data together leads to redundancy and update anomalies.

Identified Functional Dependencies (FDs):

-user_id → user_first_name, user_last_name, user_email
-wedding_id → wedding_date, wedding_budget, user_id
-venue_id → venue_name, venue_type, venue_capacity
-booking_id → venue_id, wedding_id, booking_date, start_time, end_time

=== Step 1: Decomposition to 1NF (First Normal Form) ===

Definition of 1NF:

-A relation is in 1NF if all attributes contain atomic values
-No repeating groups or multivalued attributes exist
-Each row is uniquely identifiable by a key

The relation is decomposed based on entity responsibility while preserving all data.

=== R1: USER ===

|| Table || Attributes ||
|| R1 || user_id, user_first_name, user_last_name, user_email ||

Primary Key:
-user_id

Functional Dependency:
-user_id → user_first_name, user_last_name, user_email

Justification:
-All attributes are atomic
-All attributes depend only on user_id
-user_id uniquely identifies a system user
-No repeating groups exist

Conclusion:
-R1 satisfies 1NF

=== R2: WEDDING ===

|| Table || Attributes ||
|| R2 || wedding_id, wedding_date, wedding_budget, user_id ||

Primary Key:
-wedding_id

Foreign Key:
-user_id → USER(user_id)

Functional Dependency:
-wedding_id → wedding_date, wedding_budget, user_id

Justification:
-Each wedding is uniquely identified by wedding_id
-user_id represents ownership of the wedding
-All non-key attributes depend solely on wedding_id

Conclusion:
-R2 satisfies 1NF

=== R3: VENUE ===

|| Table || Attributes ||
|| R3 || venue_id, venue_name, venue_type, venue_capacity ||

Primary Key:
-venue_id

Functional Dependency:
-venue_id → venue_name, venue_type, venue_capacity

Justification:
-Venue attributes describe a single independent entity
-Attributes are static and not dependent on other relations
-venue_id uniquely identifies a venue

Conclusion:
-R3 satisfies 1NF

=== R4: VENUE_BOOKING ===

|| Table || Attributes ||
|| R4 || booking_id, venue_id, wedding_id, booking_date, start_time, end_time ||

Primary Key:
-booking_id

Foreign Keys:
-venue_id → VENUE(venue_id)
-wedding_id → WEDDING(wedding_id)

Functional Dependency:
-booking_id → venue_id, wedding_id, booking_date, start_time, end_time

Justification:
-A booking represents a reservation of a venue for a specific wedding
-booking_id uniquely identifies each reservation
-All attributes depend directly on booking_id

Conclusion:
-R4 satisfies 1NF