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philosophy (logic)

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I need to know if these two statements are independent:

All winners are losers.
All losers are winners.

I am thinking that they are because I don't see that the truth or falsity of one tells anything about the truth or falsity of the other.

Also, if "Some Americans are children" is false, is the statement "Some nonchildren are nonAmericans" true, false, or undetermined.

I know that the statements are not logically equivalent, but I don't know what that says about the contrapositive in terms of truth value.

  • philosophy (logic) -

    I agree with your first statement.

    Your second statement about nonchildren would be undetermined.

    To use another example:

    Some bears are purple. (false)
    Some nonbears are not purple. (undetermined)

  • philosophy (logic) -

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  • philosophy (logic) -

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