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:

Yea-Saying

The tendency of respondents to agree with statements or questions regardless of their actual opinion, often leading to bias in survey responses.

Loaded

A term used to describe questions or statements that are designed to elicit emotional responses or include assumptions, potentially biasing the response.

Simplistic

An approach or explanation that oversimplifies a concept or issue, often ignoring complexities and nuances.

Double-Barreled

A term often used to describe questions that address two distinct issues simultaneously, which can cause confusion and muddy the response.