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:

Cellular Respiration

The metabolic process by which cells convert nutrients into energy (ATP), involving the oxidation of food molecules and the release of waste products.

Citric Acid Cycle

The Citric Acid Cycle, also known as the Krebs cycle, is a series of chemical reactions used by all aerobic organisms to release stored energy through the oxidation of acetyl-CoA derived from carbohydrates, fats, and proteins.

Cellular Respiration

Cellular respiration is a biochemical process in cells where organic molecules are broken down to release energy for use by the cell.

Oxidation

A chemical reaction in which a substance combines with oxygen, often producing energy in the form of heat and light.