Write the Compound Statement in Symbols $q \rightarrow \sim p$

question 14

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 I exercise, then I won?t eat too much.

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

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Definitions:

Individual Choice

Decision-making by individuals based on their preferences, resources, and trade-offs they face.

Productive Capacity

The maximum output that an economy can produce without increasing inflation, driven by available resources and technology.

Specialization

The focus of a business, region, or individual on producing a limited range of goods or services to gain greater efficiency and productivity.

Eighteenth-Century

A period in history ranging from the year 1701 to 1800, characterized by significant developments in politics, philosophy, science, and arts.