Prove each of the following statements about the integers. If 3n is even, then n is even.?

Answer 1

if 3n is even then there exist integer k such that 3n=2k so
n=2k-2n=2(k-n) so n is even!!!!

Answer 2

i'm going to do certainly one of them. you may decide something by utilising following the occasion. enable's teach #3) that 5 + 7 + 9 + ... + (2n+3) = n(n+4) Induction. Is it authentic for n = a million? 5 = a million(a million+4) = 5. Proved for n = a million. Now, assume that is authentic for the case "n-a million". Is it authentic for "n", too? 5 + 7 + .. + (2(n-a million) + 3) = (n-a million)((n-a million)+4) = (n-a million)^2 + 4(n-a million) = n^2 - 2n + a million + 4n - 4 upload 2(n) + 3 to the two facets: LHS = 5 + 7 + ... + 2n+3. RHS = (n-a million)((n-a million)+4) + 2n+3 = n^2 - 2n + a million + 4n - 4 + 2n + 3 = n^2 +4n = n(n+4) Proved

Answer 3

Odd X Odd = Odd
If n was odd then 3n would be odd since 3 is odd.
Thus n must be even

Answer 4

3n is NOT always even. For example:

let n = -1;

then... 3x1 = -3

-3 is not EVEN.. Is it?

it will only be even if n is an absolute value (positive integers)...