Changes between Version 8 and Version 9 of P5

Timestamp:

05/08/26 20:12:50 (3 weeks ago)

Author:

211171

Comment:

--

P5

@@ -258 +258 @@
 
 The final schema consists of 17 fully normalized relations.
-
-= Proof of Candidate Key =
-
-== Definition ==
-
-A set of attributes X is a candidate key if:
-
-X⁺ = R
-X is minimal
-
-The closure X⁺ is computed by repeatedly applying functional dependencies until no additional attributes can be derived.
-
-== Step 1 – Testing Single Attribute Candidate Keys ==
-
-=== Attempt 1 ===
-
-K = {attendance_id}
-
-=== Closure ===
-
-(attendance_id)⁺ gives:
-
-attendance_status
-table_number
-guest_id
-event_id
-
-Using additional dependencies:
-
-event_id → event_type, wedding_id
-guest_id → guest_first_name, guest_last_name, rsvp_status, wedding_id
-wedding_id → date, budget, notes, user_id
-user_id → first_name, last_name, email, phone_number, gender, birthday
-
-=== Missing Dependencies ===
-
-The closure still does NOT determine:
-
-venue booking information
-photographer booking information
-band booking information
-registrar booking information
-priest and church information
-
-Therefore:
-
-(attendance_id)⁺ ≠ R
-
-Conclusion:
-
-attendance_id is NOT a candidate key.
-
-== Step 2 – Testing Two Attributes ==
-
-K = {attendance_id, priest_id}
-
-=== Closure ===
-
-Additional attributes derived:
-
-priest_name
-priest_contact
-church_id
-church_name
-church_location
-
-=== Missing Dependencies ===
-
-Still missing:
-
-venue booking information
-photographer booking information
-band booking information
-registrar booking information
-
-Therefore:
-
-(attendance_id, priest_id)⁺ ≠ R
-
-Conclusion:
-
-K is NOT a candidate key.
-
-== Step 3 – Testing Three Attributes ==
-
-K = {
-attendance_id,
-venue_booking_id,
-photographer_booking_id
-}
-
-=== Closure ===
-
-Additional attributes derived:
-
-venue information
-photographer information
-wedding information
-user information
-
-=== Missing Dependencies ===
-
-Still missing:
-
-band booking information
-registrar booking information
-priest/church information
-
-Therefore:
-
-K⁺ ≠ R
-
-Conclusion:
-
-K is NOT a candidate key.
-
-== Step 4 – Testing Larger Attribute Sets ==
-
-K = {
-attendance_id,
-priest_id,
-venue_booking_id,
-band_booking_id
-}
-
-=== Missing Dependencies ===
-
-Still missing:
-
-photographer booking information
-registrar booking information
-
-Therefore:
-
-K⁺ ≠ R
-
-Conclusion:
-
-K is NOT a candidate key.
-
-== Step 5 – Including All Booking Branches ==
-
-K = {
-attendance_id,
-venue_booking_id,
-photographer_booking_id,
-band_booking_id,
-registrar_booking_id
-}
-
-=== Missing Dependencies ===
-
-Still missing:
-
-priest information
-church information
-
-Therefore:
-
-K⁺ ≠ R
-
-Conclusion:
-
-K is NOT a candidate key.
-
-== Step 6 – Final Candidate Key ==
-
-K = {
-attendance_id,
-venue_booking_id,
-photographer_booking_id,
-band_booking_id,
-registrar_booking_id,
-priest_id
-}
-
-=== Closure ===
-
-Using all functional dependencies:
-
-attendance branch is determined
-event branch is determined
-guest branch is determined
-wedding branch is determined
-venue booking branch is determined
-photographer booking branch is determined
-band booking branch is determined
-registrar booking branch is determined
-priest branch is determined
-church branch is determined
-
-No attributes remain undetermined.
-
-Therefore:
-
-K⁺ = R
-
-Conclusion:
-
-K is a candidate key.
-
-== Minimality Proof ==
-
-A candidate key must be minimal.
-
-Removing any attribute from K causes loss of at least one independent entity branch:
-
-|| Removed Attribute || Lost Information ||
-|| attendance_id || attendance branch ||
-|| venue_booking_id || venue booking branch ||
-|| photographer_booking_id || photographer booking branch ||
-|| band_booking_id || band booking branch ||
-|| registrar_booking_id || registrar booking branch ||
-|| priest_id || priest/church branch ||
-
-Therefore every attribute in K is necessary.
-
-== Why church_id Is Not Included ==
-
-Suppose we define:
-
-K = {
-attendance_id,
-venue_booking_id,
-photographer_booking_id,
-band_booking_id,
-registrar_booking_id,
-priest_id,
-church_id
-}
-
-This violates minimality because:
-
-priest_id → church_id
-
-church_id is already derivable from priest_id.
-
-Therefore church_id is redundant.
-
-The resulting set would be a superkey, NOT a candidate key.
-
-== Final Candidate Key ==
-
-K = {
-attendance_id,
-venue_booking_id,
-photographer_booking_id,
-band_booking_id,
-registrar_booking_id,
-priest_id
-}
-
-This key:
-
-Determines all attributes of R
-Is minimal
-Satisfies the formal definition of a candidate key