Question

Prove that n is odd if and only if 3n + 6 is odd by contradiction.

Answer 1

Explanation:

o - odd number

e - even number

n + e =o, if n is odd...rule 1

n + e = e, if n is even...rule 2

n × o = o, if n is odd...rule 3

n × o = e, if n is even...rule 4

thus if 3n +6 = o,

then 3n must be odd, following rule 1

=> 3n = o, then n is an odd number, following rule 3