So I created normalization steps for this pet and owner table in a database class :

Started with Candidate keys, followed by functional dependency break the tables up into tables , then the referential integrity and the end .
PET (Petname,PetType,PetBreed,PetDOB,OwnerLastnameOwnerFirstName,
OwnerPhone,OwnerEmail,Service,Date,Charge)

Step 1: Candidate Keys
The last functional dependency assumes a pet is seen at most on one day and that there is no standard charge for a service.

(PetName,Date)

Step 2 : Functional Dependecies
PetName í (PetType, PetBreed, PetDOB, OwnerLastName, OwnerFirstName, OwnerPhone, OwnerEmail)
OwnerPhone í (OwnerLastName, OwnerFirstName, OwnerEmail)
(PetName, Date) í (Service, Charge)

Step 3:
Dividing the relation if determinant is not a candidate key
Is every determinant a candidate key ?

PetName and OwnerPhone are determinants but not candidate keys

OWNER (OwnerPhone, OwnerLastName, OwnerFirstName, OwnerEmail)
PET (PetName, PetType, PetBreed, PetDOB, OwnerPhone)
SERVICE (PetName, Date, Service, Charge)

OwnerPhone in PET must exist in OwnerPhone in OWNER

PetName in SERVICE must exist in PetName in PET

i need help with Appling the normalization process to the following relations. I need the following steps like the Table above for each relation:
1. Show the candidate keys from the original relation.
2. Show the functional dependencies from the original relation.
3. Is any determinant not a candidate key? If so, show the following:
1. The new normalized relations.
2. The primary key in each new relation.
3. The foreign keys in the new relations.
4. The referential integrity constraints for the foreign keys.
Relation 1:
This relation is about home appliances, such as refrigerators, stoves, ovens, washers, dryers, etc.
" APPLIANCE (ApplianceType, BrandName, ModelNumber, SerialNumber, OwnerName, OwnerAddress, OwnerPhone)
" Assumptions:
o Each model number is unique to its brand and type. For example, a Kenmore washer could have a model number of KEN-WASH-990.
o Serial numbers are just numbers, like 12345678, so could be duplicated.
o Owner phone numbers are unique.
o State any other assumptions you make.
Relation 2:
This relation is about playgroups for children. Any child can belong to any playgroup. Each playgroup meets at a certain parent's home. That parent is the playgroup leader.
" PLAYGROUP (ParentName, ParentEmail, ParentAddress, ChildName, PlayGroup, GroupLeader)
" Assumptions:
o Each parent has a unique e-mail address.
o Each playgroup has a unique name.
o Each playgroup has only one leader.

Relation 1:

Step 1: Candidate Keys
(ApplianceType, ModelNumber)

Step 2: Functional Dependencies
(ApplianceType, ModelNumber) -> (BrandName, SerialNumber, OwnerName, OwnerAddress, OwnerPhone)

Step 3: Dividing the relation if determinant is not a candidate key
The determinant (OwnerPhone) is not a candidate key.

New Normalized Relations:
APPLIANCE (ApplianceType, BrandName, ModelNumber)
OWNER (OwnerPhone, OwnerName, OwnerAddress)

Primary Key in each new relation:
APPLIANCE: (ApplianceType, ModelNumber)
OWNER: (OwnerPhone)

Foreign Keys in the new relations:
APPLIANCE: OwnerPhone is a foreign key referencing OWNER(OwnerPhone)

Referential Integrity Constraints for the foreign keys:
APPLIANCE.OwnerPhone must exist in OWNER.OwnerPhone

Relation 2:

Step 1: Candidate Keys
(ParentEmail)

Step 2: Functional Dependencies
(ParentEmail) -> (ParentName, ParentAddress, ChildName, PlayGroup, GroupLeader)

Step 3: Dividing the relation if determinant is not a candidate key
There are no determinants that are not candidate keys.

New Normalized Relations:
PLAYGROUP (ParentEmail, ParentName, ParentAddress, PlayGroup, GroupLeader)
CHILD (ParentEmail, ChildName)

Primary Key in each new relation:
PLAYGROUP: (ParentEmail)
CHILD: (ParentEmail, ChildName)

Foreign Keys in the new relations:
CHILD: ParentEmail is a foreign key referencing PLAYGROUP(ParentEmail)

Referential Integrity Constraints for the foreign keys:
CHILD.ParentEmail must exist in PLAYGROUP.ParentEmail

Sure, I can help you with that. Here are the normalization steps for each of the given relations:

Relation 1: APPLIANCE (ApplianceType, BrandName, ModelNumber, SerialNumber, OwnerName, OwnerAddress, OwnerPhone)

Step 1: Candidate Keys
- (ApplianceType, BrandName, ModelNumber, SerialNumber)
- OwnerPhone

Step 2: Functional Dependencies
- (ApplianceType, BrandName, ModelNumber, SerialNumber) -> (OwnerName, OwnerAddress, OwnerPhone)
- OwnerPhone -> (OwnerName, OwnerAddress)

Step 3:
- PetName and OwnerPhone are determinants but not candidate keys.

New Normalized Relations:
APPLIANCE (ApplianceType, BrandName, ModelNumber, SerialNumber, OwnerPhone)
OWNER (OwnerPhone, OwnerName, OwnerAddress)

Primary Key(s):
- APPLIANCE: (ApplianceType, BrandName, ModelNumber, SerialNumber)
- OWNER: OwnerPhone

Foreign Key(s):
- APPLIANCE: OwnerPhone references OWNER(OwnerPhone)

Referential Integrity Constraints:
- OwnerPhone in APPLIANCE must exist in OwnerPhone in OWNER

Relation 2: PLAYGROUP (ParentName, ParentEmail, ParentAddress, ChildName, PlayGroup, GroupLeader)

Step 1: Candidate Keys
- ParentEmail
- PlayGroup

Step 2: Functional Dependencies
- ParentEmail -> (ParentName, ParentAddress)
- PlayGroup -> (GroupLeader)

Step 3:
- ParentEmail and PlayGroup are determinants and candidate keys.

No further normalization is required for this relation.

I hope this helps! Let me know if you have any further questions.

For Relation 1:

Step 1: Candidate Keys
The candidate keys for this relation can be determined based on unique identifiers. In this case, we can consider the combination of (BrandName, ModelNumber) as a candidate key, as each appliance has a unique brand and model number.

Candidate Key: (BrandName, ModelNumber)

Step 2: Functional Dependencies
Based on the given information, we can identify the following functional dependencies:

ApplianceType -> BrandName, ModelNumber
OwnerPhone -> OwnerName, OwnerAddress

Functional Dependencies:
1. ApplianceType -> BrandName, ModelNumber
2. OwnerPhone -> OwnerName, OwnerAddress

Step 3: Determinant Analysis
In this step, we check if any determinant is not a candidate key. If so, we need to create new normalized relations.

In this case, all determinants are candidate keys. Therefore, we do not need to create new normalized relations.

Normalization for Relation 1:

APPLIANCE (ApplianceType, BrandName, ModelNumber, SerialNumber, OwnerName, OwnerAddress, OwnerPhone)

Relation 2:

Step 1: Candidate Keys
The candidate keys for this relation can be determined based on unique identifiers. In this case, we can consider the combination of (ParentEmail, PlayGroup) as a candidate key, as each parent can be associated with multiple playgroups, and each playgroup has a unique name.

Candidate Key: (ParentEmail, PlayGroup)

Step 2: Functional Dependencies
Based on the given information, we can identify the following functional dependencies:

ParentEmail -> ParentName, ParentAddress
PlayGroup -> GroupLeader

Functional Dependencies:
1. ParentEmail -> ParentName, ParentAddress
2. PlayGroup -> GroupLeader

Step 3: Determinant Analysis
In this step, we check if any determinant is not a candidate key. If so, we need to create new normalized relations.

In this case, all determinants are candidate keys. Therefore, we do not need to create new normalized relations.

Normalization for Relation 2:

PLAYGROUP (ParentName, ParentEmail, ParentAddress, ChildName, PlayGroup, GroupLeader)

In summary, both Relation 1 and Relation 2 do not require further normalization as all determinants are candidate keys.