Construct a Truth Table for the Statement $\sim ( p \rightarrow q ) \rightarrow ( p \wedge \sim q )$

question 215

Multiple Choice

Construct a truth table for the statement.
- $\sim ( p \rightarrow q ) \rightarrow ( p \wedge \sim q )$

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

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Definitions:

Logical Not Operator

A unary operator (!) that inverts the truth value of its operand.

Expressions True

Refers to expressions in programming that evaluate to a Boolean true value.

Resulting Condition

The state or outcome produced after the execution of a particular operation or set of operations in programming.

Opposite State

Refers to a condition or value that is directly in contrast or opposition to another.