Translate the Statement into Symbols Then Construct a Truth Table $\mathrm{p}=$

question 163

Multiple Choice

Translate the statement into symbols then construct a truth table.
- $\mathrm{p}=$ Parker will work in an office.
$\mathrm{q}$ = Parker will work as a forest ranger.
$\mathrm{r}=$ Parker will work as a landscape architect.
Parker will not work in an office, but he will work as a forest ranger or a landscape architect.

• A)
• \(\begin{array} { l l l c }
• \mathrm { p } & \mathrm { q } & \mathrm { r } & \sim \mathrm { p } \wedge ( \mathrm { q } \vee \mathrm { r } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\
• \mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\
• \mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
• \end{array}\)
• B)
• \(\begin{array} { l l l c }
• \mathrm { p } & \mathrm { q } & \mathrm { r } & \sim \mathrm { p } \wedge ( \mathrm { q } \vee \mathrm { r } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\
• \mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }
• \end{array}\)
• C)
• \(\begin{array} { c c c c }
• \mathrm { p } & \mathrm { q } & \mathrm { r } & \sim \mathrm { p } \wedge ( \mathrm { q } \vee \mathrm { r } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\
• \mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\
• \mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
• \end{array}\)
• D)
• \(\begin{array} { c c c c }
• \mathrm { p } & \mathrm { q } & \mathrm { r } & \sim \mathrm { p } \wedge ( \mathrm { q } \vee \mathrm { r } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\
• \mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\
• \mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }
• \end{array}\)

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