I don't like basketball "and /or/ nor" football

[hereinchina]

Hello,
I'm not sure if I should use the word "and", "or", or "nor" in the following sentences, marked number one, two and three below, or if all three words are grammatically correct. I think that you can only use the word "and" for the positive, i.e. I like Chinese food and French food. I think you need to use the word "or" or "nor" for the negative.
1. I don't like basketball and football.
2. I don't like basketball or football.
3. I don't like basketball nor football.

[fluffyhamster]

2 certainly sounds the most natural; 3 is a bit formal~strange. 1 is just a proposition-combining~ellipting (I don't like basketball and [I don't like] basketball) and probably somewhat less usual way of expressing the meaning of 2, in which the 'or' isn't doing much other than simply combining the object nouns rather than whole propositions (??/*I don't like basketball or I don't like football); 2's 'or' thus has no force in any "choice-meaning" sense, cf. Do you want coffee or tea? (You are unlikely to want both at the same time)). Even if the 'or' here were stressed (I don't like basketball OR football, so I'm not playing either!), it still wouldn't be equating to an "either-or" choice, but rather to a set-forming~combining meaning. But the easiest thing might be to just read the sentences as all saying "I-don't like-[either of] these two sports".

[hereinchina]

Hello Fluffyhamster,
Thank you very much for taking the time to answer my question.
Best wishes,