Construct a Truth Table for the Statement $\sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim t \wedge \mathrm{s}))$

question 267

Multiple Choice

Construct a truth table for the statement.
- $\sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim t \wedge \mathrm{s}) )$

• A)
• \(\begin{array}{ccccc}
• \mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) & \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} \\
• \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\
• \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
• \end{array}\)
• B)
• \(\begin{array}{lcccc}
• \mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\
• \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\
• \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\
• \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
• \end{array}\)
• C)
• \(\begin{array}{ccccc}
• \mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\
• \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\
• \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
• \end{array}\)
• D)
• \(\begin{array}{cccc}
• \mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \\
• \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\
• \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\
• \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\
• \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\
• \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \\
• \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
• \end{array}\)

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Definitions:

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The male reproductive cell or gamete, which is necessary for fertilization of the female ovum, leading to the development of an embryo.

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Molecules like DNA or RNA in living organisms that carry genetic information critical for inheritance, function, and development.

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Structures found within cells that carry genetic information in the form of genes.

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External factors or conditions that affect an individual's development, behavior, or lifestyle, including social, physical, and cultural factors.