6. Determine if the following pairs of functions are of the same order. Justify your answers. (a) $f(x)=\log _{10} x$ and $g(x)=\log _{2} x$ (b) $f(x)=\left\lfloor x+\frac{1}{2} ight floor and $g(x)=7 x$ (c) $f(x)=\sqrt{x^{3}} \log x$ and $g(x)=x^{2}$ 7. In each case, decide if the given argument is valid. Justify your answers. (a) $$ \begin{aligned p & \vee all p\wedge eg q&W \therefore \quad p \oplus q & \end{aligned} $$ (b) $$ \begin{aligned} p & \vee all 9 & ightarrow r \hline \therefore p & ightarrow r \end{aligned} $$ CS.SD1451