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

question 16

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
-If the food is good or if I eat too much, I?ll exercise.

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

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Definitions:

Subjective Approach

An approach to making decisions or assessments that relies on individual preferences, emotions, or thoughts, instead of objective data or proof.

WACC

Weighted Average Cost of Capital; a calculation of a firm's cost of capital in which each category of capital is proportionately weighted, representing the average cost of funding from all sources.

Pure Play

A company that focuses on a specific industry or product segment without diversification into other areas.

Capital Structure

The combination of borrowing and ownership funds that a business employs to finance its activities and expansion.