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

---

Definitions:

Raw Materials Inventory

The total value of all the materials that have not yet been used in the production process.

Raw Materials Production

The initial stage in the manufacturing process, involving the extraction or creation of raw materials to be used in production.

Budgeted Production

The number of units planned to be produced in a certain period according to a company's budget.

Budgeted Sales

Projected sales revenue for a given period based on market analysis and company objectives.