A：Forgive me, I didn’t mean to offend you.
      对不起。我不是有意要冒犯你的。

B：Never mind about that.
      没关系。

1. 冒犯；得罪；触怒
    If you offend someone, you say or do something rude which upsets or embarrasses them.

    e.g. He apologizes for his comments and says he had no intention of offending the community...
           他为自己发表的评论道歉并称无意冒犯该社群。
    e.g. The survey found almost 90 percent of people were offended by strong swearwords...
           这项调查发现几乎90％的人都会为不堪入耳的脏话所触怒。

2. 违反，违犯，违背（法律、规定、原则等）
    To offend against a law, rule, or principle means to break it.

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    e.g. This bill offends against good sense and against justice...
           该法案有悖于理智和公正。
    e.g. In showing contempt for the heavyweight championship Douglas offended a stern code.
           道格拉斯藐视重量级拳王称号的行为违背了严格的准则。

3. 犯罪；犯法
    If someone offends, they commit a crime.

    e.g. In Western countries girls are far less likely to offend than boys.
           在西方国家，女孩的犯罪倾向远低于男孩。