It's been a little why since I've had discrete math, so could someone help me remember why:

"There exists an 'x' such that for all 'y', x + y == 0" is FALSE,

but

"For all 'x', there exists a 'y' such that x + y == 0" is TRUE?

Thanks!

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- Jan 31st 2008, 09:59 AMjtc4zHQuantifiers question
It's been a little why since I've had discrete math, so could someone help me remember why:

"There exists an 'x' such that for all 'y', x + y == 0" is FALSE,

but

"For all 'x', there exists a 'y' such that x + y == 0" is TRUE?

Thanks! - Jan 31st 2008, 10:25 AMcolby2152
Read it twice over and slowly. The first statement says that there is one number, $\displaystyle x$ that when added to any number $\displaystyle y$, it equals zero. You cannot possibly say that both $\displaystyle x+4=0$ and $\displaystyle x+55=0$.

The second line says that for any number $\displaystyle x$, there exists a y that satisfies those conditions. This is a one-to-one relationship. For:

$\displaystyle x=5$,

$\displaystyle y=-5$;

for $\displaystyle x=$http://www.virginiaapples.org/images/top-apple.gif,

$\displaystyle y=-$http://www.virginiaapples.org/images/top-apple.gif.