Attempting to identify transitive dependency

Question

Hello I am attempting to identify a transitive dependency in the following diagram. I think that possibly the determinate of "Subtotal" is "Quantity" and "Price Charged" but I'm not sure if "subtotal" is also dependant on the "product_code" which would make it a partial dependency right?

This is how I've worked out the 1NF.

1NF (CUTOMER_NUMBER, INVOICE_NUMBER, PRODUCT_CODE → CUSTOMER_NAME, INVOICE_DATE, LINE_NUMBER, COMMON_NAME, SCIENTIFIC_NAME, CATEGORY, QUANTITY, PRICE_CHARGED)
PARTIAL DEPENDENCIES:
CUSTOMER (CUSTOMER_NUMBER → CUSTOMER_NAME)
INVOICE (INVOICE_NUMBER → INVOICE_DATE)
PRODUCT (PRODUCT_CODE → COMMON_NAME, SCIENTIFIC_NAME, QUANTITY, PRICE_CHARGED)
TRANSITIVE DEPENDENCY
SUBTOTAL (QUANTITY, PRICE_CHARGED → SUBTOTAL)

I'm fairly confident about the other dependencies but am not sure the transitive one is correct?

edit: MODIFIED DETAIL

1NF (CUTOMER_NUMBER, INVOICE_NUMBER, PRODUCT_CODE → CUSTOMER_NAME, INVOICE_DATE, LINE_NUMBER, COMMON_NAME, SCIENTIFIC_NAME, CATEGORY, QUANTITY, PRICE_CHARGED)
PARTIAL DEPENDENCIES:
CUSTOMER (CUSTOMER_NUMBER → CUSTOMER_NAME)
PRODUCT (PRODUCT_CODE → COMMON_NAME, SCIENTIFIC_NAME)
INVOICE (INVOICE_NUMBER, LINE_NUMBER → QUANTITY, PRICE_CHARGED, INVOICE_DATE, PRODUCT_CODE)
TRANSITIVE DEPENDENCY
-   ?

Is this looking better, is there no transitive dependency?

Answer 1

Can you get a different answer for subtotal for any specific pair of quantity and price_charged? No, of course not. Arithmetic is arithmetic.

Quantity and price charged depend on invoice_number and line_number, not on product_code at all. In fact, product_code also depends on invoice_number and line_number.

EDIT:

Partial Dependencies are dependencies on part of a multi-part key. Transitive Dependencies are things that depend on non-key attributes. Step one is to look at your initial relation and determine what the key of the whole thing is, or if there are multiple candidate keys, what they are.

Here are the pieces that I'd guess make up your key, based on the limited sample data and some common sense:

• Invoice Number
• Line Number

Your table looks to me like an invoice detail table to me. This means that if you know what invoice and which line on the invoice, you know which distinct record you're looking at. If that's the case, what do each of the non-key columns depend on? Let's look at each in turn:

• CUTOMER_NUMBER: depends on just the INVOICE_NUMBER, therefore PARTIAL.
• PRODUCT_CODE: depends on the whole key, therefore FULL
• CUSTOMER_NAME: depends on CUSTOMER_NUMBER (non-key), therefore TRANSITIVE
• INVOICE_DATE: depends on just the INVOICE_NUMBER, therefore PARTIAL.
• COMMON_NAME: depends on PRODUCT_CODE (non-key), therefore TRANSITIVE.
• SCIENTIFIC_NAME and CATEGORY (ditto)
• QUANTITY: depends on the whole key, therefore FULL.
• PRICE_CHARGED: depends on PRODUCT_CODE (non-key), therefore TRANSITIVE.

As noted previously, SUBTOTAL is calculated based on QUANTITY and PRICE_CHARGED so it depends on the full key as well.