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# Answer the exercise given below.\begin{aligned} & \left\{\begin{array}{l} \text { Everyone that is at least } 16 \text { years old is eligible } \\ \text { for a driver's license. } \\ \text { Mable is not eligible for a driver's license. } \end{array}\right. \\ & \therefore \text { Mable is not at least 16 years old. } \end{aligned}a. Is this a valid argument? Why or why not?b. Is this conclusion true? In other words, is it the case that every person who is not eligible for a driver's license is under 16 years of age? Why or why not?c. Is it possible to answer yes to Part a and no to Part b? Why or why not?

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$\begin{array}{ c l } \mathbf{a.} & \begin{array}{l} \mathrm{To\ determine\ whether\ argument\ is\ valid,\ do\ the\ following:}\\ \\ \mathbf{First,\ identify\ statements\ }\boldsymbol{p}\mathbf{\ and\ }\boldsymbol{q} :\\ \mathrm{In\ this\ case} \ \begin{array}{ c l } \boldsymbol{p} & \mathrm{represents} \ \mathrm{the\ statement} \ 'A\ \mathrm{person} ,x,\ \mathrm{is\ at\ least\ 16\ years\ old} '.\\ \boldsymbol{q} & \mathrm{represents} \ \mathrm{the\ statement} \ 'x\ \mathrm{is\ eligible\ for\ for\ a\ drivers\ license} '. \end{array}\\ \\ \mathbf{Next,\ make\ the\ following\ observations} :\\ \mathrm{The\ second\ statement\ is\ a\ particular\ form\ of} \ \ '\mathbf{not} \ \boldsymbol{q} '\\ \mathrm{The\ third\ statement\ is\ a\ particular\ form\ of} \ '\mathbf{not} \ \boldsymbol{p} ':\\ \\ \mathbf{Next,\ write\ the\ statements\ in\ the\ form\ of\ an\ argument:}\\ \mathrm{\begin{array}{ l } \begin{cases} \mathrm{If} \ \boldsymbol{p} \ \mathrm{then} \ \boldsymbol{q}\\ \boldsymbol{q} \end{cases}\\ \therefore \boldsymbol{p} \end{array}}\\ \\ \mathrm{Observe\ its\ structure\ is\ consistent\ with} \ \mathrm{Law\ of\ Indrect\ Reasoning\ which\ shows\ the\ argument\ is\ }\boxed{\mathrm{valid}} . \end{array} \end{array}$

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