Construct a Truth Table for the Statement $(\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s})$

question 88

Multiple Choice

Construct a truth table for the statement.
- $(\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s})$

• A)
• \(\begin{array}{ccc}
• \mathrm{r} & \mathrm{S} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{S} \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{F} \\
• \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{F} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{T}
• \end{array}\)
• B)
• \(\begin{array}{lll}
• \mathrm{r} & \mathrm{s} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s}) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{F} & \mathrm{T} & \mathrm{F} \\
• \mathrm{F} & \mathrm{F} & \mathrm{T}
• \end{array}\)
• C)
• \(\begin{array}{lll}
• \mathrm{r} & \mathrm{S} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{S}) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{F} & \mathrm{T} & \mathrm{F} \\
• \mathrm{F} & \mathrm{F} & \mathrm{F}
• \end{array}\)
• D)
• \(\begin{array}{lll}
• \mathrm{r} & \mathrm{s} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s}) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{F} \\
• \mathrm{T} & \mathrm{F} & \mathrm{F} \\
• \mathrm{F} & \mathrm{F} & \mathrm{F} \\
• \mathrm{F} & \mathrm{T} & \mathrm{T}
• \end{array}\)

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