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中学数学教学大纲指出,要把集合、对应等思想适当渗透到教材中去。用集合的思想来说明“充要条件”,不仅简单明瞭,而且能加深理解。本文中,为了叙述方便,我们把满足数学条件A、B的集合也分别记为集合A、B。1.如果集合A是B的真子集,即AB,则条件A是B的充分条件而非必要条件,B是A成立的必要条件而非充分条件。例1 因为{矩形}{平行四边形},所以“四边形是矩形”是“四边形是平行四边形”的充
High school mathematics syllabus pointed out that the collection, correspondence and other ideas should be properly infiltrated into teaching materials. To illustrate the “necessary and sufficient conditions” with a set of ideas is not only straightforward but also helps to deepen understanding. In this paper, for the convenience of description, we also consider the set of mathematical conditions A, B are also recorded as a set A, B. 1. If set A is a true subset of B, AB, then condition A is a sufficient condition of B, not a necessary condition, and B is a necessary condition of A, not a sufficient condition. Example 1 Because of {Rectangle} {Parallelogram}, “Quadrangle is a rectangle” is “Quadrangle is Parallelogram”