Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top
  1. Points R,S and T are collinear and T is not a point on the centered at R with radius RS Negation: Points R,S and T are not collinear and T is a point on the center at R with radius RS

is this correct?

  1. Given a line l and a point P that is not on l, there is exactly one line through P that is parallel to l Negation: Given a line l and a point p that is on l, the is at least one line through P that is not parallel to l

is this correct? Thank you

share|cite|improve this question
Tip: You may both upvote helpful answers, and/or accept one answer for each question you ask: to accept an answer: click on the greyed out $\checkmark$ to the left of the answer. To "upvote" an answer, click on the greyed-out "up-arrow" right above the answer's vote count (left of answer). Both upvoting and accepting answers are ways of "thanking" the answerer(s), and accepting an answer rewards both you and the answerer, with additional points. – amWhy Feb 8 '13 at 22:11

Re (1), NO. The negation of a proposition of the form $A$ and $B$ is either not-$A$ or not-$B$ (and not not-$A$ and not-$B$).

Re (2), NO. For a start the negation of there is exactly one F is there are either no F's or more than one F.

There are interesting issues lurking in the background in the second case about how to construe the Given ... construction, but we can probably ignore them here.

share|cite|improve this answer
Perhaps "Given $A$ and $B$" means $\forall A\,\forall B$ – Trevor Wilson Jan 24 '13 at 17:05
For more on negations of compound statements, see's_laws. – Austin Mohr Jan 24 '13 at 17:17

Not correct, to negative and statement negate both sides and use or instead of maintaining and.

($A$ and $B)^{n}$ = ($A^{n}$ or $B^{n}$)

($A$ or $B)^{n}$ = ($A^{n}$ and $B^{n}$)

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.