# Math Help - negations

1. ## negations

Hi everyone,

Could someone please tell me what the negation of "If and only if" would be? -p V -q :?

Is the negation of "If T is continuous, then T is bounded" T is continuous and T is not bounded
or T is not continuous and T is bounded.

For the statement "I can eat dinner or go to the show," that would be "I cannot eat dinner and I cannot go to the show,right?"

Thank you very much

2. $\neg \left( {p \Leftrightarrow q} \right) \equiv \left( {\neg p \wedge q} \right) \vee \left( {p \wedge \neg q} \right)
$

3. Could you tell me if this is correct based on that?

The number x is prime only if x is odd

P: the number x is prime
Q: x is odd

P arrow q. This negated would be (-P ^ Q) V (P ^ -Q) That is, it would read "The number x is not prime and q is odd or x is prime and x is not odd

Thank you

4. Originally Posted by chocolatelover
The number x is prime only if x is odd
P: the number x is prime
Q: x is odd
P arrow q. YES

This negated would be (-P ^ Q) V (P ^ -Q) NO
Just (P ^ -Q)
See the above.

5. In words this would be "The number x is prime or x is not odd," right?

Thank you

6. Originally Posted by chocolatelover
In words this would be "The number x is prime or x is not odd," right?
NO! The number x is prime and x is not odd.