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Sufficiency and Necessity in Language and Math

  1. Jun 15, 2015 #1
    In english language i use sufficiency and necessity interchangeably to mean the same thing (is that right?) this is now preventing me from understanding the conditional connectives, and i fear i might end up remembering what each of the conditional statements mean (eg: for "Q is necessary condition for P" i could just remember that what comes first is the consequent) but i wanted it to come as naturally as the rest of the logical connectives. So can someone close the gap between the math and language here?

    Thanks :)
  2. jcsd
  3. Jun 15, 2015 #2


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    No, they are not the same at all. Sufficient means it will do something but is not necessary and other things might do that thing just as well. Necessary means you can't do the thing without it.
  4. Jun 15, 2015 #3


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    No, sufficient and necessary are not the same.

    Sufficient means that if some condition is true then some result is true.
    Necessary means that if some condition is not true then some result is not true.

    It is necessary to leave my house in order to go to my office. If I do not leave my house I cannot go to the office. But it is not sufficient. If I leave my house other things have to happen before I get to the office.

    If I go to the office then I have left my house. It is sufficient to know that I have left my house if I know that I have arrived at the office. But it is not necessary, since other things could indicate I have left my house.
  5. Jun 15, 2015 #4


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    To clarify, in logical language:
    "P is sufficient for Q" ≡ P→Q
    "P is necessary for Q" ≡ Q→P (which is the contrapositive of ~P→~Q from DEvens's post)
  6. Jun 16, 2015 #5
    Thank you all, it was just a linguistic error on my part :)
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