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

question 103

Multiple Choice

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

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

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Definitions:

Monopolist

An individual or entity that has exclusive control over the supply of a particular good or service, potentially influencing prices and market conditions.

Duopoly

An oligopoly where only two firms dominate the market or industry, often resulting in competitive or strategic behavior.

Oligopoly

A market structure characterized by a small number of firms whose control over the market is significant enough to influence prices and other market factors.

Cournot Duopoly

A market structure where two firms compete with each other by choosing quantities to produce independently.