QuestionB. Construct a truth table for the symbolic statement in part $A$. \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline p & q & $\sim p$ & $\sim q$ & $\mathrm{p} \rightarrow \sim \mathrm{q}$ & \multicolumn{2}{|l|}{$\sim p \leftrightarrow q$} & \multicolumn{2}{|l|}{$(p \rightarrow \sim q) \wedge(\sim p \rightarrow q)$} \\ \hline T & T & f & f & & & & & \\ \hline T & F & f & t & & & & & \\ \hline F & T & t & f & & & & & \\ \hline F & F & t & t & & & & & \\ \hline \end{tabular}

Studdy Solution
Here's our completed truth table:
$\begin{array}{ccccccc} p & q & \sim p & \sim q & p \rightarrow \sim q & \sim p \leftrightarrow q & (p \rightarrow \sim q) \wedge (\sim p \rightarrow q) \\ \text{T} & \text{T} & \text{F} & \text{F} & \text{F} & \text{F} & \text{F} \\ \text{T} & \text{F} & \text{F} & \text{T} & \text{T} & \text{T} & \text{T} \\ \text{F} & \text{T} & \text{T} & \text{F} & \text{T} & \text{T} & \text{T} \\ \text{F} & \text{F} & \text{T} & \text{T} & \text{T} & \text{F} & \text{F} \\ \end{array}$