# Quantifiers question

• Jan 31st 2008, 09:59 AM
jtc4zH
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!
• Jan 31st 2008, 10:25 AM
colby2152
Quote:

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