1. ## Quantifiers 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!

2. Originally Posted by jtc4zH
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!
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 $\displaystyle x=$,
$\displaystyle y=-$.