Write the Compound Statement in Symbols $p \rightarrow q$ B) $\mathrm{p} \rightarrow \mathrm{q}$

question 177

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 eat too much, then I?ll exercise.

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

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Definitions:

Median

The middle value in a data set, arranging the data in ascending order, or the average of the two middle values if the dataset is even.

SAT Scores

SAT Scores are standardized test results used for college admissions in the United States, assessing mathematical, reading, and writing skills.

Standard Deviation

A measure of dispersion or variability that quantifies how much individual data points deviate from the mean of a dataset.

Normally Distributed

Referring to a bell-shaped curve distribution where data are symmetrically distributed around the mean, implying most data points are close to the mean and fewer are near the extremes.