contrapositive of this statement?

• Sep 21st 2012, 06:44 AM
bonfire09
contrapositive of this statement?
"If a and b are consecutive odd numbers, then a+b is an even number." I was thinking it was "If a+b is an odd number then a or b is a nonconsecutive even integer". I thought this mean the same as "If a+b is an odd number then a and b are not consecutive odd integers"? I was thinking these two sentences mean the same thing because either a or b or both are nonconsective even integers?
• Sep 21st 2012, 07:27 AM
emakarov
Re: contrapositive of this statement?
The phrase "nonconsecutive integer" does not make sense. Only two or more integers can be consecutive or not.

"If a+b is an odd number then a and b are not consecutive odd integers" is correct.
• Sep 21st 2012, 07:59 AM
bonfire09
Re: contrapositive of this statement?
Oh ok. and Im guessing that "...then a and b are not consecutive odd integers" means that both a and b are even integers that are not consecutive?
• Sep 21st 2012, 08:12 AM
emakarov
Re: contrapositive of this statement?
Quote:

Originally Posted by bonfire09
Oh ok. and Im guessing that "...then a and b are not consecutive odd integers" means that both a and b are even integers that are not consecutive?

No, for example, the following pairs of numbers are not consecutive odd integers: (1, 5), (1, 2), (2, 4) and (2, 6). Of those pairs, only the last one consists of even integers that are not consecutive.A pair of numbers does not consist of consecutive odd integers either when the numbers are odd but not consecutive, or if at least one of them is even.