Thread: 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!

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, that when added to any number , it equals zero. You cannot possibly say that both and .

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

for ,
.