Construct a Truth Table for the Statement $(r \wedge p) \wedge(\sim p \vee t)$

question 85

Multiple Choice

Construct a truth table for the statement.
- $(r \wedge p) \wedge(\sim p \vee t)$

• A)
• \(\begin{array} { c c c c }
• \mathrm { r } & \mathrm { p } & \mathrm { t } & ( \mathrm { r } \wedge \mathrm { p } ) \wedge ( \sim \mathrm { p } \vee \mathrm { t } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\
• \mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\
• \mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\
• \mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\
• \mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
• \end{array}\)
• B)
• \(\begin{array} { c c c c }
• \mathrm { r } & \mathrm { p } & \mathrm { t } & ( \mathrm { r } \wedge \mathrm { p } ) \wedge ( \sim \mathrm { p } \vee \mathrm { t } ) \\
• \hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\
• \mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\
• \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\
• \mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\
• \mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\
• \mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }
• \end{array}\)

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Definitions:

Exponentiation

The mathematical operation involving the raising of one number to the power of another.

Division

A mathematics operation where a number is divided into parts or segments, represented by the division sign (/ or ÷).

Division

A fundamental mathematical operation that represents the process of dividing one number by another.

Exponentiation

A mathematical operation involving the raising of a base to the power of an exponent, symbolizing repeated multiplication.