Homework Help: Negate the following sentences

1. Aug 30, 2010

joemama69

1. The problem statement, all variables and given/known data

Negate the sentence

2. Relevant equations

3. The attempt at a solution
a) I will do my hw and i will pass this class
N: i will not do my hw or i will not pass.

b) seven is an integer and seven is even
N: seven is not an integer or is seven even.

c)if T is continuouse, then t is bounted.
N:T is continiouse and not bounded

d)i can eat dinner or go to the show
N:i cant eat dinner and cant go to the show.

e) if x is odd, then x is prime
N: x is not odd and it is not prime

f)the number x is prime only if x is odd
N: not sure what to do w/ the only if(<->) part.

g)If i am not home, then sam will asnwer the phone and he will tell you how to reach me.
N:i am not home and sam wont answer or tell you how to reach me.

h)if the stars are green or the white hourse is shining, then the world is eleven feet wide
N: the stars are green and the horse is not shining and the world is not eleven ft wide.

2. Aug 31, 2010

HallsofIvy

Re: Negating

Okay, the negation of "p and q" is "not p or not q".

Surely you mean "seven is NOT even".

Yes, the negation of "if p then q" is "p and not q"
(But I don't think there is an "e" on the end of "continuous".)

Good. The negation of "p or q" is "not p and not q".

[quote) if x is odd, then x is prime
N: x is not odd and it is not prime[/quote]
No, look back to c. The hypothesis should NOT be negated.

"p only if q" is the same as "if q then p". But that is NOT "<- >". Did you mean "the number x is prime if and only if x is odd"? The negation of "p if and only if q" is "(p and not q) or (not p and q)" .

This is of the form "if p then (q or r)". Use what I said before.

This is of the form "if (p or q) then r". The negation would be, as before "(p and q) and not r" which is exactly what you have.

Mostly well done. Just a couple of errors.