Construct a Truth Table for the Statement $\sim(p \rightarrow q) \rightarrow(p \wedge \sim q)$

question 72

Multiple Choice

Construct a truth table for the statement.
- $\sim(p \rightarrow q) \rightarrow(p \wedge \sim q)$

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

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