Wednesday

July 30, 2014

July 30, 2014

Posted by **audryana** on Wednesday, September 27, 2006 at 8:09pm.

a)a proof by contraposition

b)a proof by contradiction

I'll try part b, you'll have to refresh me on what contraposition means here.

Here is the claim we start with

If n is an integer and 3n+2 is even, then n is even.

Reduction as absurdum or proof by contradiction begins by assuming the conclusion is false and then showing this contradicts one of the premises, thereby showing the conclusion is true.

Suppose n is odd, then 3n is odd since the product of odd integers is an odd int. Every odd int. + and even int. is odd. Show this by adding 2k+1 + 2m = 2(k+m)+1 = an odd number. Therefore 3n+2 is an odd number, but this contradicts the assumption that 3n+2 is even. Therefore if 3n+2 is even then n is even.

I think contraposition would be: If n is even then 3n+2 is even. You should be able to do this I think.

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