Answer to Question #171052 in Discrete Mathematics for kapil

Question

) (P ∧ Q ∧ R) ∨ (¬P ∧ R ∧ Q) ∨ (¬P ∧ ¬Q ∧ ¬R

Answer 1

$\def\arraystretch{1.5} \begin{array}{|c|c|c|c|c|c|c|c} P & Q & R & P \land Q \land R & \neg P \land R \land Q & \neg P \land \neg Q \land \neg R & (P \land Q \land R) \lor (\neg P \land R \land Q) \\ \hline 0 & 0 & 0 & 0 & 0 & 1 & 0\\ \hline 0 & 0 & 1 & 0 & 0 & 0 & 0\\ \hline 0 & 1 & 0 & 0 & 0 & 0 & 0\\ \hline 0 & 1 & 1 & 0 & 1 & 0 & 1\\ \hline 1 & 0 & 0 & 0 & 0 & 0 & 0\\ \hline 1 & 0 & 1 & 0 & 0 & 0 & 0\\ \hline 1 & 1 & 0 & 0 & 0 & 0 & 0\\ \hline 1 & 1 & 1 & 1 & 0 & 0 & 1\\ \hline \end{array}$

$$\def\arraystretch{1.5} \begin{array}{|c|} (P \land Q \land R) \lor (\neg P \land R \land Q) \lor (\neg P \land \neg Q \land \neg R) \\ \hline 1 \\ \hline 0 \\ \hline 0\\ \hline 1 \\ \hline 0 \\ \hline 0\\ \hline 0 \\ \hline 1\\ \hline \end{array}$$