SOLUTION: Help with a proof, please. Here is the example and solution: Q: Show that if n is an integer and n3 + 5 is odd, then n is even using a proof by contraposition. A: Assume that

Algebra ->  Matrices-and-determiminant -> SOLUTION: Help with a proof, please. Here is the example and solution: Q: Show that if n is an integer and n3 + 5 is odd, then n is even using a proof by contraposition. A: Assume that      Log On


   

Question 930281: Help with a proof, please.
Here is the example and solution:
Q: Show that if n is an integer and n3 + 5 is odd, then n is even using
a proof by contraposition.
A: Assume that n is odd, so n=sk+1 for some integer k.
Then n^3+5 =2(4k^3 + 6k^2+ 3k + 3)
Since n^3 + 5 = 2x some integer, it is not odd.
This is the question:
Q: Prove that if n is an integer and 3n + 2 is even, then n is even using
a proof by contraposition.
A: Assume that n is even, so n = sk for some integer k.
Then 3n+2 <
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Use 2 instead of s. You want to assume on the contrary that there exists an odd integer n such that 3n+2 is even. Then n = 2k+1 for some integer k, and 3(2k+1)+2 = 6k+5 = 2(3k+2)+1 which is not even.