Write the Compound Statement in Symbols $(r \wedge p) \rightarrow q$

question 187

Multiple Choice

Write the compound statement in symbols. Then construct a truth table for the symbolic statement.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-The food is good and if I eat too much, then I?ll exercise.

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

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Definitions:

Marginal Cost

The cost of producing one additional unit of a good or service, crucial for decision-making in production and pricing strategies.

Average Variable Cost

The total variable costs of production (costs that change with output level) divided by the quantity of output produced, indicating the variable cost per unit of output.

Average Fixed Cost

The fixed costs of production (those that do not change with the level of output) divided by the quantity of output produced.

Average Total Cost

The cost of producing one unit, calculated by dividing the entire production cost by the quantity of units made.