为了简明地表达命题中条件和结论的逻辑关系,在数学命题中的条件可分为充分条件、必要条件和充要条件。它们的意义是:如果A成立,那么B成立即A(?)B,这时我们就说条件A是B成立的充分条件,也就是说,为使B成立,具备条件A就足够了。如果B成立,那么A成立,即B(?)A,或者,如果A不成立,那么B就不成立,这时我们就说,条件A是B成立的必要条件,也就是说,要使B成立,就必须具备有条件A。若既有A(?)B,又有B(?)A,那么A既是B成 In order to concisely express the logical relationship between the conditions and conclusions in the proposition, the conditions in mathematical propositions can be divided into sufficient conditions, necessary conditions and necessary and sufficient conditions. Their meaning is: If A is true, then B is A (?) B, and then we say that condition A is a sufficient condition for B to be established, that is to say, to satisfy B, condition A is sufficient. If B holds, then A holds, that is, B (?) A, or, if A does not hold, then B does not hold. Then we say that condition A is a necessary condition for B to be established, that is to say, It must have a conditional A. If both A (?) B, B (?) A, then A is B into