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:

Real GDP

Gross Domestic Product adjusted for inflation, representing the value of all goods and services produced over a specific period, measured in constant prices.

Aggregate Demand Curve

A curve depicting the total demand for all goods and services in an economy at various price levels, assuming all other factors remain constant.

Short-Run Aggregate Supply Curve

A curve that shows the relationship between the price level and the quantity of goods and services supplied in the economy in the short term, assuming input costs remain constant.

Short-Run Equilibrium

The price level and real GDP that result when the aggregate demand curve intersects the short-run aggregate supply curve.