*Or* can be used to mean:

* *Logical or*: A *or* B is true when A is true, B is true, or both are true and false when A and B are false.
* *Exclusive or*: A *xor* B is true when A is true,  B is true, and no other cases.

For instance see here[1].

Either can be used in common speech. In law, there is often case law that argues for one over the other. This has been held as true in [patent law][2], where the *xor* variety can be assumed when the *or* logical operator is argued. Typically one writing a patent would rephrase to avoid the use of *or* entirely, although not everyone follows that advice.

The use of either can cause problems semantically. For instance:

> Assume *I like milk in my coffee* is true.
>
> Assume *I like motor oil in my coffee* is false.
>
> Then *I like milk or motor oil in my coffee* by either definition above is true.

This, however, doesn't match common usage. In that common usage, *or* actually means *and*, because both paths must be true for the conclusion to follow.

The answer to your question is that either interpretation can be defended, or both, or neither, depending on context.

  [1]: https://krissparks.medium.com/and-or-xor-bitwise-operators-2ae3fbcfa5bc#:~:text=Now%20the%20OR%20operator%20is,then%20the%20result%20is%20true.&text=Lastly%2C%20the%20XOR%20(exclusive%20OR,then%20the%20result%20is%20false.
  [2]: https://adamslaw.biz/2015/12/patent-claim-drafting-use-of-or/#:~:text=%E2%80%9COr%E2%80%9D%20may%20mean%3A%20A,Kustom%20Signals%2C%20Inc.