I am learning logic now and I realized that the word 'or' in my language actually means XOR, not or.
Is this true also in English?
When someone says for example : "my car is red or a Mercedes" I believe that the listener actually perceives that if the car is red then it is not a Mercedes and vice versa.
Is there a word in English language that actually represents correctly the mathematical 'or' concept?
On
It is not true that in spoken language, "or" always means XOR. It ultimately depends on context as well as intonation. For example, if I ask, "Do you have a pen or pencil that I could borrow?" do you really perceive this as XOR?
In spoken language, and for that matter, even in formal written mathematics, we often make the logic more precise through careful phrasing. Compare:
Would you like cake or ice cream? Or both?
You can have either cake or ice cream. Which would you prefer?
Finally, it would represent a kind of communication breakdown to interpret such questions too literally. If I ask whether you want cake or ice cream, and your answer is "yes", then you're being cheeky. This is also good for cheap humour in science fiction where robots learn to talk.
Short answer: no.
Sometimes English speakers will say something like 'either P or Q' to try an express an exclusive or, but even that expression cannot be assumed to express an exclusive or. For example, if I say: 'when I am old, I want to be either rich or happy', don't think that I would mind being both rich and happy!