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不少同学对数学命题的逻辑关系一直比较模糊,常常将充分性与必要性混为一谈,弄不清充分、必要条件的逻辑关系而出现错误在同学们的学习中也经常发生.如“甲是乙的充分条件”与“甲的充分条件是乙”就是完全不同的两种逻辑关系;“甲是乙的充要条件”与“甲的充要条件是乙”都表示甲与乙是等价关系,但从充分性的角度来看,前者的充分性是指“甲是乙的充分条件”,后者的充分性是指“甲的充分条件是乙”.初学的同学特别易出现差错.例1α+β>4,αβ>4,是α>2,β>2,的什么条件?
Many students have been ambiguous about the logic of mathematical propositions, often confusing sufficiency with necessity, and failing to understand the logical relationship between sufficient and necessary conditions. Errors often occur in the learning of students. For example, “A is B. The sufficient condition of ”and“ sufficient condition of A is B” is a completely different logical relationship; “the necessary and sufficient conditions of A and B” and “the necessary and sufficient condition of A is B” both mean that A and B are equivalence relations However, from the perspective of adequacy, the adequacy of the former refers to “A is a sufficient condition for B,” while the adequacy of the latter means that “A sufficient condition is B.” Beginners are particularly prone to errors. 1α+β>4, αβ>4, what condition is α>2,β>2,?