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

question 103

Multiple Choice

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

• A)
• \(\begin{array} { c c c }
• \mathrm { p } & \mathrm { r } & ( \mathrm { p }
• _\rightarrow \sim \mathrm { r } ) \rightarrow ( \mathrm { p } \wedge \sim \mathrm { r } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { T } & \mathrm { F } & \mathrm { T } \\
• \mathrm { F } & \mathrm { T } & \mathrm { F } \\
• \mathrm { F } & \mathrm { F } & \mathrm { F }
• \end{array}\)
• B)
• \(\begin{array} { c l c }
• \mathrm { p } & \mathrm { r } & ( \mathrm { p }_ \rightarrow \sim \mathrm { r } ) \rightarrow ( \mathrm { p } \wedge \sim \mathrm { r } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { T } & \mathrm { F } & \mathrm { T } \\
• \mathrm { F } & \mathrm { T } & \mathrm { F } \\
• \mathrm { F } & \mathrm { F } & \mathrm { T }
• \end{array}\)
• C)
• \(\begin{array} { c c c }
• \mathrm { p } & \mathrm { r } & ( \mathrm { p } \rightarrow \sim \mathrm { r } ) \rightarrow ( \mathrm { p } \wedge \sim \mathrm { r } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { T } & \mathrm { T }
• \end{array}\)
• D)
• \(\begin{array} { c c c }
• \mathrm { p } & \mathrm { r } & ( \mathrm { p } \rightarrow \sim \mathrm { r } ) \rightarrow ( \mathrm { p } \wedge \sim \mathrm { r } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { T } \\
• \mathrm { F } & \mathrm { T } & \mathrm { T } \\
• \mathrm { F } & \mathrm { F } & \mathrm { T }
• \end{array}\)

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Definitions:

Principle Due

The portion of a loan or mortgage payment that reduces the original amount borrowed; it does not include interest or additional fees.

Interest Rate

The percentage of an amount of money charged for its use per a certain period, often annually, by a lender to a borrower.

Compounded Annually

A method of calculating interest where the interest earned each year is added to the principal, forming a new base for future interest calculations.

Mortgage

A type of loan typically used to purchase real estate, where the property itself serves as collateral for the loan.