Let c ∈ Z: Write a detailed structured proof to prove the statement:
c^5 + 7 is even, then c is odd.
I started out like this:
Assume c ∈ Z Assume c^5 + 7 == 2n Then c == 2n + 1
Also, is this claim true? I plugged in odd numbers for c, and haven't encountered a counter-example. Is there a way to determine the veracity of the claim before doing the proof?