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Contrapositive

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12 Mar 2012, 09:36
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Can anyone help, I have the following Contrapositive but not sure how to prove it

If n is not even then n^2 is not divisible by 6

thanks
hazzy
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12 Mar 2012, 09:46
hazzy wrote:
Can anyone help, I have the following Contrapositive but not sure how to prove it

If n is not even then n^2 is not divisible by 6

thanks
hazzy

That's not correct: consider $$n=\sqrt{6}\neq{even}$$ but $$n^2=6$$, which IS divisible by 6.

If we are told that n is an integer then it's correct: if n is not even then it's odd, odd^2=odd which can not be divisible by any number which has 2 as a factor, or simply n^2=odd so it's not divisible by 2, hence it can not be divisible by 6=2*3.

Hope it's clear.
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12 Mar 2012, 09:56
In order for a number to be divisible by 6, the number should be divisible by 2 and 3.
Now coming to the problem, it is stated that n is not even which makes it Odd.

Then n^2 is odd
Since 2 is not factor of any odd integer, hence 6 is not factor of n^2.

This holds true when n is an integer.

Hope it helps.
Re: Contrapositive   [#permalink] 12 Mar 2012, 09:56
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