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\title{Math 240 Overleaf Form}
\author {Jose Delgado}
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\fancyhead[R]{Jose Delgado \\ Math 240, Proof 2}
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\begin{center} \Large Linear Algebra: Proofs\end{center}
\begin{section} {Proof-A-Day, January 16}
{\bf Claim:} If n is a positive integer, then n is odd if and only if 5n+6 is odd.
\begin{proof}
Suppose there is a positive integer n. Assume that the result of 5n+6 is odd. 5n+6 can be rewritten as 5(n+1)+1. We know that any integer plus one results in a switched polarity (even becomes odd and odd becomes even), so the equation 5(n+1) must be even. Because five is an odd integer, the result of n+1 must be even because an odd integer times an even integer always results in an even integer. This means that n must be an odd integer.
Therefore, n is odd if and only if 5n+6 is odd.
\end{proof}
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