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Having trouble paraphrasing sentence

Philosophy Asked by larry mintz on December 22, 2020

F: French wins gold medal

G: Germans win gold medal

D: Danish win gold medal

I have to use truth connectives to paraphrase:

They will not all win gold medals

I am thinking when paraphrasing it ,
one country can win and two loose or
Two win and one loose

Am I on the right path?

One Answer

You can parse "Not all win golds medals" as "At least one does not win a gold medal." Either way, you can parse as:

~(F & G & D)

Which is truth-functionally equivalent to:

(~F v ~G v ~D)

Both are consistent with all three losing, two losing and one winning, or one losing and two winning.

Answered by John Beverley on December 22, 2020

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