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I am confused about something.

How do you differentiate the partial and total function?

I know that partial functions do not use the whole domain, but how do you know if the whole domain will be used?

For example, I want to define an operation for the AUDI car company and I want to define the function between audi car and owner. So I declare a set CAR and a set PERSON.

The function CAR ---> PERSON is partial or total and why?

Also, when I declare a set do I mean that the set can contain all the items that might exist in the world?

Thanks