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有一道这样的试题——原命题:末位数字是数字或5的整数,能被5整除;它的否命题是( )。这道题简单似看,却颇有一定的深度,对初中学生来讲是要求较高的一道题。对这道题,考生的答案绝大多数是:末位数字不是0或5的整数,不能被5整除。连标准答案上也是如此回答的,很多老师也坚持认为这是一个正确答案。可见这是一种很有代表性的错误。问题主要就出在原命题题设中的“或”上。用字母来表示,其一般形式是:若A_1或A_2,则B。这里只要A_1、A_2中有一个成立,则B也成立。下面我们来证明“若(?)或(?),则(?)”不是原命题
There is a question like this - the original proposition: the last digit is a number or an integer of 5 and can be divisible by five; its no proposition is (). This question is simple, but it has a certain degree of depth. It is a higher-demanding question for junior high school students. For this question, most of the candidates’ answers are: The last digit is not an integer of 0 or 5 and cannot be divisible by five. Even the answer to the standard answer, many teachers also insist that this is a correct answer. This shows that this is a very representative error. The problem lies mainly in the “or” of the original propositional design. Expressed in letters, the general form is: If A_1 or A_2, then B. Here, as long as one of A_1 and A_2 holds, B also holds. Let us prove that if “(?) or (?), then (?)” is not the original proposition