I'm working with a proof in a discrete structures CS course, and I am a little confused by how to build up some logic for the argument. Currently we're working with symbolic logic, the problem statement is:
"For all integers n, if n is an odd integer, then $ 3n^2$ is also an odd integer."
So far I know I can build this problem by stating the two following things:
- Prove all odd numbers, multiplied by $3$ remain odd. (how can I go about proving this?)
- Prove all odd numbers square also remain odd.
What would be the best way about proving this? Would it be simpler to prove all numbers multiplied by an odd number remain odd (since an odd number squared is still being multiplied by an odd number)
I'm not really looking for a solution to be handed to me, I just feel a little stuck on where to go from here, and would like some direction on what to do next.
Thanks ahead of time guys!