Write the Compound Statement in Symbols $q \rightarrow \sim p$

Write the compound statement in symbols. Then construct a truth table for the symbolic statement.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If I exercise, then I won?t eat too much.

A) $q \rightarrow \sim p$
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \mathrm { q } \rightarrow \sim \mathrm { p } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

B) $\sim(p \rightarrow q)$
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \sim ( \mathrm { p }\rarr \mathrm { q } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\ \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

C) $\sim(p \rightarrow q)$
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \rightarrow \mathrm { q } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

D) $\mathrm{q} \rightarrow \sim \mathrm{p}$
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \mathrm { q } \rightarrow \sim \mathrm { p } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$

Correct Answer:

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