Math  /  Discrete

QuestionConstruct a truth table for the given statement. [(qp)(pq)](pq)[(q \rightarrow p) \wedge(p \wedge q)] \leftrightarrow(p \wedge q)
Complete the truth table. \begin{tabular}{|c|c|c|c|c|c|} \hlinepp & q\mathbf{q} & qp\mathbf{q} \rightarrow \mathbf{p} & pq\mathbf{p} \wedge \mathbf{q} & (qp)(pq)(q \rightarrow p) \wedge(p \wedge q) & {[(qp)(pq)](pq)[(q \rightarrow p) \wedge(p \wedge q)] \leftrightarrow(p \wedge q)} \\ \hlineTT & TT & t & t & t & t \\ \hline T & F & \square & \square & \square & \\ \hline \end{tabular}

Studdy Solution
pqqppq(qp)(pq)[(qp)(pq)](pq)TTTTTTTFTFFTFTFFFTFFTFFT\begin{array}{cccccc} p & q & q \rightarrow p & p \wedge q & (q \rightarrow p) \wedge (p \wedge q) & [(q \rightarrow p) \wedge (p \wedge q)] \leftrightarrow (p \wedge q) \\ T & T & T & T & T & T \\ T & F & T & F & F & T \\ F & T & F & F & F & T \\ F & F & T & F & F & T \\ \end{array}

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