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充要条件是揭示命题与命题关系的重要概念,为了便于说明充要条件的两个性质,我想首先依据六年制高中代数第一册第44页摘要叙述它的定义: 如果“从命题A成立可以推得命题B成立”,即如果有“A(?)B”,那么我们说命题A是命题B成立的充分条件; 如果“从命题B成立可以推得命题A成立”,即如果有“B(?)A”,那么我们说命题A是命题B成立的必要条件; 如果既有A(?)B,又有B(?)A,即如果有A(?)B,我们就说A是B成立的充分而且必要条件,简称充要条件。上述定义强调了A、B是“命题”,这与十年制高中数学第二册第110页的定义相比,我感到提
The necessary and sufficient condition is an important concept to reveal the relationship between propositions and propositions. In order to explain the two properties of the necessary and sufficient conditions, I want to first describe its definition based on the summary of the first six pages of the six-year senior high school algebra: If “From the proposition A The establishment of a proposition B can be set up, that is, if there is ”A(?)B“, then we say that proposition A is a sufficient condition for the establishment of proposition B; if ”from the establishment of proposition B can be derived from proposition A is established“, ie if there is ”B(?)A", then we say that proposition A is a necessary condition for the establishment of proposition B; if there is both A(?)B and B(?)A, ie if there is A(?)B, we say A is a sufficient and necessary condition for the establishment of B, and the abbreviation is a sufficient and necessary condition. The above definition emphasizes that A and B are “propositions”. Compared with the definition of 110th page of the 10th-year high school mathematics book, I feel that