考验你的思维能力：一类含有if P then Q句式的逻辑问题

    今天回学校，有人说我智商降低了。我仔细想了一下，这段时间的数理思考确实少了些；但也不能说我完全废了，我还出了一次模拟赛的题呢。摆脱应试教育的思维模式后，不知道我的智商是上升了还是下降了。我开始在想如何检测我的思维是否还和原来一样敏捷。
    刚才看到OIBH上又在讨论数理逻辑，然后网上找到了这几道逻辑题来想。实践证明，我的思维能力仍然还不错。我把这些题目写在下面大家可以试一下。
    这是一类问题，这类问题的命题中包含有条件判断的形式。

Following are several problem from the island of knights and knaves where knights always tell truth whereas knaves always lie.

   1. A makes the following statement: "If I am a knight then so is B." What are A and B?
   2. Someone asks A, "Are you a knight?" He replies, "If I am a knight then I'll eat my hat". Must he eat his hat?
   3. A says, "If I am a knight then 2+2=4." Is A a knave or a knight?
   4. A says, "If B is a knight then I am a knave." What are A and B?