Find the contrapositive. If there exists real numbers x and y with x y and then f is not one-to-one

I got:

if f is one-to-one then for all real numbers x and y with x=y or

Why is it still = and not ?

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- Sep 8th 2011, 09:46 PMJskiddon't understand part of answer to contrapositive question
Find the contrapositive. If there exists real numbers x and y with x y and then f is not one-to-one

I got:

if f is one-to-one then for all real numbers x and y with x=y or

Why is it still = and not ? - Sep 8th 2011, 10:26 PMpickslidesRe: don't understand part of answer to contrapositive question
Hey Jskid

When thinking about the contrapositive consider this.

The original statement: if m then n

Then the contrapositive will be: if not n then not m.

does this help?

P.S. to avoid those nasty latex errors use "tex" tags not "math" tags. - Sep 8th 2011, 11:09 PMJskidRe: don't understand part of answer to contrapositive question
- Sep 9th 2011, 03:51 AMemakarovRe: don't understand part of answer to contrapositive question
We have .

Should be: "...then for all real numbers x and y, it is the case that x=y or ." (The phrase "it is the case that" is inserted just to avoid two mathematical expressions with no words between them.) Alternatively, "...then for all real x and y, if , then ."

What is "still" = ?. The assumption was ; its negation is .

Yes, but without the initial "If."

The last equation does change to inequation. - Sep 12th 2011, 12:52 AMJskidRe: don't understand part of answer to contrapositive question
The answer key has

If f is one-to-one, then for all real numbers x and y either x=y or

is the end a typo? Shouldn't it be ? - Sep 12th 2011, 02:27 AMemakarovRe: don't understand part of answer to contrapositive question
Yes, I think so.