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\item \textbf{Obtain a contradiction by taking n to be the smallest positive integer for which (2) is true, and so conclude that $\sqrt{2}$ is not a rational number.}  \\Smallest positive integer $n> 0$ is when n = 1. Then $1\sqrt{2}$ = $\sqrt{2}$  There \\There  are no two positive integers for p,q where $\sqrt{2} = \frac{p}{q}$ \frac{p}{q}$.  \\ $\therefore \sqrt{2} is irrational. $  \item \textbf{Convert the above into a structured proof that $\sqrt{2}$ is not a rational number.}  \item \textbf{Show that $\log _2(3)$ is not a rational number.}