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

question 151

Multiple Choice

Translate the statement into symbols then construct a truth table.
- $\mathrm{p}=$ The garden contains sunflowers.
$\mathrm{q}=$ The fence is painted white.
$\mathrm{r}=$ The lawnmower is electric.
The garden contains sunflowers or the fence is painted white, or the lawnmower is electric.

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

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