Distributing 'Not' over a ConjunctionDate: 09/18/2003 at 11:22:31 From: Sarah Subject: logic If p = today is sunny and q = tomorrow is Friday then which of the following means "It is not true that today is sunny and tomorrow is Friday"? 1. not (p^q) or 2. not p ^ q I'm not sure whether "it is not true" in front of a conjuction applies to both conjuncts or only the first one. Date: 09/18/2003 at 23:22:09 From: Doctor Achilles Subject: Re: logic Hi Sarah, Translations are always tricky. However, I would say that "it is not true that ..." means that the negation applies to everything that follows. Contrast It is not true that today is sunny and tomorrow is Friday with Today is not sunny and tomorrow is Friday In the sentence I just made up, the 'not' is only in the first clause, and so only applies to 'p'. In your sentence, the 'not' governs the whole thing, so should apply to 'p' and 'q'. So the correct translation is not (p^q) I hope this helps. If you have other questions or you'd like to talk about this some more, please write back. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994-2015 The Math Forum
http://mathforum.org/dr.math/