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Doubt in "If then must" condition

Do the right wayDo the right way Alum Member
in Logic Games 181 karma

Hi 7Sages,

I have a confusion in representing "if then must" conditions.

Suppose there is a sentence given as :
If N is not selected then T must be selected .

So, is the representation like this?
not N -> T
contrapositive is
not T -> N

If here, N is satisfied then does the rule drops away and does T becomes a floater ?

Since there is a 'must' keyword involved..I am confused.

Please clarify this.
Thank you.

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Comments

  • paulmv.benthempaulmv.benthem Alum Member
    1032 karma

    Everything you've written looks correct to me! And, yes, assuming there are no other rules bearing on "T," if "N" is satisfied, "T" becomes a floater.

  • TexAgAaronTexAgAaron Alum Member
    1723 karma

    Yes you are correct.

    /N->T
    /T->N

    The "if" signals a sufficient condition and the must signals a necessary condition. Your application of satisfying N in the contrapositive example is spot on too. By satisfying the necessary condition, you make the sufficient (T) a floater.

  • olepuebloolepueblo Alum Member
    235 karma

    Looks good. You could substitute “is” for “must be” if that is useful.

  • Do the right wayDo the right way Alum Member
    181 karma

    Thanks everyone for clarifying the doubt. I understood that 'must' and 'can' could be substituted with 'is' and the same rules follows. :)

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