1 give a clear and concise proof of this proposition 2 given

1. give a clear and concise proof of this proposition.

2. given the propostion above, provide a clearly written, analogous bi-conditional statement regarding even integers. write a seprate proof for this statement.

3. write a clearly written corollary to parts 1 and 2 that describes te relationship between n^3 and n, where n is any positive integer. you do not need to prove the corollary, but it should be wriiten in bi-conditional form.

Solution

propositon:- let m,n,k belongs to \\mathbb{N}. The product mnk is odd if and only if m,n and k are all odd.
1. give a clear and concise proof of this proposition.
2. given the propostion above, provide a clearly written, analogous bi-conditional statement regarding even integers. write a seprate proof for this statement.
3. write a clearly written corollary to parts 1 and 2 that describes te relationship between n^3 and n, where n is any positive integer. you do not need to prove the corollary, but it should be wriiten in bi-conditional form.