Even Integer Plus 5 is Odd/Historical Note

Historical Note on Even Integer Plus 5 is Odd

There is nothing profound about this result.

Gary Chartrand used it as a simple demonstration of the construction of various kinds of proof in his Introductory Graph Theory of $1977$.

It is questionable whether the indirect proof and the Proof by Contradiction actually constitute different proofs of this result, but both are included on $\mathsf{Pr} \infty \mathsf{fWiki}$ anyway, in case they are found to be instructional.

He sets a similar theorem as an exercise:

Prove the implication "If $x$ is an odd integer, then $y = x - 3$ is an even integer" using the three proof techniques: ...

but it has been considered not sufficiently different from this one to be actually included on $\mathsf{Pr} \infty \mathsf{fWiki}$ as a separate result to be proved.

For similar reasons, several other of the trivial exercises in applied logic that he sets have also been omitted from this site.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.5$: Theorems and Proofs: Problem Set $\text A.5$: $27$