1951 AMC 12 第 36 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
36.
下列用于证明一个几何图形是轨迹的方法中，哪一种不正确？
Which of the following methods of proving a geometric figure a locus is not correct?
轨迹上的每一点都满足条件，轨迹外的每一点都不满足条件。
Every point on the locus satisfies the conditions and every point not on the locus does not satisfy the conditions.
每个不满足条件的点都不在轨迹上，且轨迹上的每一点都满足条件。
Every point not satisfying the conditions is not on the locus and every point on the locus does satisfy the conditions.
每个满足条件的点都在轨迹上，且轨迹上的每一点都满足条件。
Every point satisfying the conditions is on the locus and every point on the locus satisfies the conditions.
轨迹外的每一点都不满足条件，且每个不满足条件的点都不在轨迹上。
Every point not on the locus does not satisfy the conditions and every point not satisfying the conditions is not on the locus.
每个满足条件的点都在轨迹上，且每个不满足条件的点都不在轨迹上。
Every point satisfying the conditions is on the locus and every point not satisfying the conditions is not on the locus.
答案：B
小提示：
轨迹证明必须同时证明“在轨迹上”与“满足条件”之间的两个方向
A locus proof needs both implications between “on the locus” and “satisfies the conditions”
大提示：
利用逆否命题判断每个选项是否证明了两个方向
Use contrapositives to see whether each choice establishes both directions
解答：
令 表示“在轨迹上”， 表示“满足条件”。完整的证明需要同时证明 和 。选项 B 先陈述 ，这只是 的逆否命题，随后又重复 。它始终没有证明 。
因此，正确答案是 B。
Let mean “on the locus” and mean “satisfies the conditions.” A complete proof needs both and Choice B states which is merely the contrapositive of and then repeats It never proves
Thus, the correct answer is B.
其他年份的第 36 题
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