Friday

October 31, 2014

October 31, 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.

**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 ...

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 ...

Geometry - Write an indirect proof. Given:n^2 is even Prove: n^2 is divisible by...