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

question 253

Multiple Choice

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

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

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Definitions:

Limited Partnership

A business structure in which one or more of the owners may be granted limited liability as long as one partner is designated as a general partner with unlimited liability.

General Partnership

A business structure in which the business owners share the management and risk of the business.

Limited Liability

A legal structure that protects company owners' personal assets from business debts and liabilities.

Legal and Administrative Costs

Expenses incurred by a business for legal services and administrative operations.