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

question 82

Multiple Choice

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

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

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Definitions:

Well-Specified End Point

A clearly defined goal or outcome that is to be achieved or reached in a process, study, or task.

Forming Subgoals

The strategy of breaking down a task into smaller, more manageable tasks in order to facilitate problem-solving.

Algorithm

A step-by-step procedure or formula for solving a problem or accomplishing a task, often used in mathematics and computer science.

Arrangement

The act of organizing or positioning objects or elements in a structured or specific order.