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Homework Statement , relevant equations, and the attempt at a solution

I was reading through Invitation to Discrete Mathematics and attempted to solve an exercise that involved a proof. I've typeset everything in LaTeX and made a PDF out of it so that it does not clutter the post. The proof seems somewhat incomplete to me, almost as if I hadn't proofed what I had to. Therefore, I would like someone to assess it for me.

This is **not** homework.

Thanks for your time.

**are all in the attached file.**I was reading through Invitation to Discrete Mathematics and attempted to solve an exercise that involved a proof. I've typeset everything in LaTeX and made a PDF out of it so that it does not clutter the post. The proof seems somewhat incomplete to me, almost as if I hadn't proofed what I had to. Therefore, I would like someone to assess it for me.

This is **not** homework.

Thanks for your time.