Databases normalization in 2NF - mysql

Question

I'm normalizing at the moment in 2NF and I'm quite confused, Here is what i have so far in 0 NF Colour is a multi valued attribute of Product
Product = Product_ID (PK)
Colour{Colour ID, Colour_Name}
Then in 1NF colour gets its own table so its
Colour=
+Colour_ID (PK)
+Product_ID (FK)
+Colour_Name
in 2NF its then changed to 2 Separate Tables
Colour =
+Colour_ID (PK)
+Product_ID(FK)
and a new table
Product_Colour =
+Colour_ID
+Colour_Name
I'm i've finished out the ERD and doing the mySQL but are they (Colour_ID) both primary keys respectively or is one a foreign key, but if one is then a foreign key do i need a primary key for that table?
Thanks,

Answer 1

You definitely need a colour table:
colour_id INT PRIMARY KEY
colour_name VARCHAR(255) # or other appropriate data type
Then, if you know that each product will always have exactly two colours, your product table might look like this:
product_id INT PRIMARY KEY,
color1 INT NOT NULL FOREIGN KEY (colour.colour_id),
color2 INT NOT NULL FOREIGN KEY (colour.colour_id)
You could drop the second NOT NULL in case products will always have one or two colours.
The more flexible approach would be to use a third table, allowing you to add an arbitrary number of colours to each product:
product table:
product_id INT PRIMARY KEY
product_colors table:
product_id INT FOREIGN KEY (product.product_id)
colour_id INT FOREIGN KEY (colour.colour_id)
PRIMARY KEY(product_id, colour_id)
So, in this case, both id fields are foreign keys on their own while together forming the primary key so it's impossible to add the same colour to the same product twice.
(pseudo SQL syntax used)

Answer 2

I visualize this:
Product = Product_ID (PK), Colour_ID (FK)
Colour = Colour_ID (PK), Colour_Name
________________________ _________________________
| Product_ID | Colour_ID | | Colour_ID | Colour_Name |
-------------------------- ---------------------------
|____________|___________| |___________|_____________|