一階邏輯題：“John has exactly one brother”的翻譯是哪一個？

Question

誰能幫我解決以下問題？

我正在努力解釋這個問題中的所有 4 個選項......

我嘗試將所有選項轉換為 CNF，但當我嘗試進行解釋時，這對我來說意義不大。

Answer 1

翻譯：

(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.

與你的陳述相對應的選項是（E）。 它不能是中間三個，因為它們都是有條件的（你說約翰有一個兄弟不是有條件的）。 (A) state 約翰有一個兄弟嗎？ 但是，它並沒有說兄弟是唯一的（只有那個存在）。 從技術上講，(A) 說約翰有一個兄弟，這個兄弟和他自己是同一個兄弟，任何至少有一個兄弟的人都可以這么說。