“如果一颗小球是红色的,那么它的颜色是确定的”的逆否命题成立吗?(来自 黑道梦境间谍

共 14 条评论

  1. Zemo

    逆命题不是”如果一颗小球的颜色是确定的,那么它使红色的”吗?

    • Zemo

      没看清,是逆否”如果一颗小球的颜色是确定的,那么它不是红色的”

  2. hub_0

    成立。
    逆否命题为:如果一个小球的颜色是不确定的,那么它不一定是红色的

    • bill_2048

      “小球的颜色是红色”这一命题的否定是“小球的颜色不是红色”。
      我认为
      不成立的原因是:这是一个简单命题。原命题和逆否命题等价的前提是复合命题。但在这里看似有“如果”“那么”可这并不是复合命题。
      目前在我看的屈婉玲的《离散数学》的数理逻辑部分中并没有明确的指出,所以我也没法自圆其说。

      • bill_2048

        不好意思,我说错了,今天重新看了一下,里面有说明:
        复合命题中原命题与其逆否命题同真假。(这里有如果那么,所以是复合命题)
        原命题:“如果一颗小球是红色的,那么它的颜色是确定的。是复合命题没错。
        逆否命题:如果一个小球的颜色不确定,那么它不是红色。
        现在我们来判断真假,1 如果这个小球颜色真的是红色,原命题显然为真。逆否命题中的条件错误,所以结论说什么都可以,即逆否命题为真。2 如果这个小球颜色随机,原命题中条件为假,结论说什么都行,即原命题为真。逆否命题显然为真。
        综上所述,原命题为真,逆否命题也成立。

    • Candy

      Well I guess I don’t have to spend the weekend fiugirng this one out!

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  3. wes2002

    逆否命题是“如果一个小球的颜色是不确定的,那么小球的颜色不是红色”。

    我觉得判断的关键在于原命题里“确定”的理解。
    一个物体颜色是“确定”的,说明它具有一种“确定的颜色”。
    由于红色是一种“确定的颜色”,如果一个小球的颜色是不确定的(小球不具有一种“确定的颜色”),那么它的颜色便不是红色。

    • ivan

      应该表述为 如果一个小球的颜色是不确定的,那么小球的颜色不一定是红色

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