They're both correct, and have different meanings. Can he swim and dive, means can this person swim, and can this person dive, if the answer is yes, he can do both. Can he swim or dive, if the answer is yes, he could only be able to swim, or only be able to dive, or both, and usually the answer will specify which. E.g: Can he swim and dive? A: Yes Can he swim or dive? A: He can swim, but cannot dive.