Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Distributing 'Not' over a Conjunction

Date: 09/18/2003 at 11:22:31
From: Sarah
Subject: logic


  p = today is sunny 


  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 


  It is not true that today is sunny and tomorrow is Friday


  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
Associated Topics:
High School Logic
Middle School Logic

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994-2015 The Math Forum