一阶逻辑题：“约翰正好有一个兄弟”的翻译是哪一个？

Question

谁能帮我解决以下问题？

我正在努力解释这个问题中的所有 4 个选项...

我尝试将所有选项转换为 CNF，但是当我尝试进行解释时，这对我来说没有更多意义。

Answer 1

翻译：

(A) There exist x and y such that x is John's brother 
    and y is John's brother and x = y.
    <=> John has a brother.

(B) If there exists x such that x is John's brother then
    every y is John's brother and x = y.
    <=> If John has a brother then the brother is the
        only person in existence.

(C) If there exists x such that x is John's brother then
    for all y if y is John's brother then y = x.
    <=> If John has a brother then he only has one.

(D) If for all x, x is John's brother, then there exists
    a y such that y is John's brother and x = y.
    <=> If everybody is John's brother then John has
        a brother.

(E) There exists an x such that x is John's brother
    and for all y, if y is John's brother, then x = y.
    <=> John has a brother and he's the only one.

与您的陈述相对应的选项是 (E)。不能是中间三个，因为它们都是有条件的（你说约翰有兄弟的说法不是有条件的）。 (A) 是否声明约翰有一个兄弟；但是，它并没有说兄弟是唯一的（只是存在一个）。从技术上讲，(A) 说约翰有一个和他自己一样的兄弟，这可以说是任何至少有一个兄弟的人。