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

prove that if n is an integer and 3n+2 is even, then n is even using

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.

## Answer this Question

## Related Questions

- Discrete Math - 1. Assume that n is a positive integer. Use the proof by ...
- discrete math - Prove by contradiction that for any even integer a and any odd ...
- DISCRETE MATHS - If m and n are integers such that mn is even, then m is even or...
- Discreet Mathematical Structures - Use proof by contraposition to prove the ...
- Math Proof - Prove that square root of 12 is irrational. **I don't know if I did...
- DISCRETE MATHS - Prove that for every set S, Ø \subseteq( S. i need to Use ...
- discrete math - 1)prove that if x is rational and x not equal to 0, then 1/x is ...
- Calculus I - Show that the equation x^4 + 4x + c = 0 has at most two real roots...
- DISCRETE MATHS - Prove that for all integers a, b, n: if n = a + b, then a < ...
- Geometry. - prove that the distance between any two points inside triangle abc ...

More Related Questions