AMC 8 1985 Problem 25
AMC8 1985 年第 25 题
逻辑推理（跨域）★★★★☆
Five cards are lying on a table as shown. Each card has a letter on one side and a whole number on the other side. Jane said, "If a vowel is on one side of any card, then an even number is on the other side." Mary showed Jane was wrong by turning over one card. Which card did Mary turn over?
如图所示，桌上放着五张卡片。每张卡片一面是字母、另一面是整数。Jane 说：「如果任何一张卡片的一面是元音字母，那么它的另一面就是偶数。」Mary 只翻开一张卡片就证明了 Jane 是错的。Mary 翻开的是哪张卡片？
- A.3
- B.4
- C.6
- D.
- E.
正确答案 · Correct Answer
A
解析 · Solution
解法1
常规解法 · 找反例
命题「有元音 背面是偶数」的反例 = 一面元音、另一面奇数。所给卡片里，只有露出奇数 3 的那张可能背面藏着元音，翻开它就能反驳，故选 A。
巧解 · 排除法
只看元音/辅音、奇/偶。偶数卡 4、6 无论背面是什么都不违反规则；辅音卡 P、Q 根本不触发规则；唯一可能成为反例的就是露出 3 的卡。
Solution 1
Elementary · find a counterexample
A counterexample to if a vowel, then an even number is a card with a vowel on one side and an odd number on the other. Among the cards, only the one showing the odd number 3 could hide a vowel, so it is the card that could disprove the claim — choice (A).
Slick · elimination
Only vowel/consonant and odd/even matter. The even cards 4 and 6 cannot violate the rule whatever is behind them, and the consonant cards P and Q never trigger it; the only possible counterexample is the card showing 3.
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