Negate the following sentences

[joemama69]

Homework Statement

Negate the sentence

Homework Equations

The Attempt at a Solution

a) I will do my homework and i will pass this class
N: i will not do my homework 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 can't eat dinner and can't 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 won't 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.

 

[HallsofIvy]

Homework Statement

Negate the sentence

Homework Equations

The Attempt at a Solution

a) I will do my homework and i will pass this class
N: i will not do my homework or i will not pass.

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

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

Surely you mean "seven is NOT even".

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

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".)

i can eat dinner or go to the show
N:i can't eat dinner and can't go to the show.

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.

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

"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)" .

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 won't answer or tell you how to reach me.

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

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.

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.