negations: what is the negation of 'if and only if' ?

[chocolatelover]

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

 

[o_O]

Re: negations

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

That doesn't quite work. An "if and only if" statement refers to a biconditional, a conditional whose converse is also true. Anyway, there's a biconditional-disjunctive equivalence: p ? q is the same as (p & q) V (~p & ~q). Makes sense right? If p is true, q must be true (p & q). If q isn't true, p cannot be true (~p & ~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.

Negated-conditional equivalence: ~(p ? q) is the same thing as p & ~q

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

Sure. The context of the statement implies that the 'or' is an exclusive one, one can be true but not the other at the same time.

Here's a reference to the equivalencies: http://faculty.washington.edu/smcohen/120/Chapter8.pdf

 

[chocolatelover]

Re: negations

Thank you very much

Regards