Construct the truth table.\begin{tabular}{|c|c|c|c|c|}\hlinep & q & r & (r∧q)∨p & (q∨p)∧r \\\hlineT & T & T & T & T \\\hlineT & T & q2 & T & q4 \\\hlineT & q2 & T & q2 & q4 \\\hlineT & q2 & q2 & q2 & q4 \\\hlineq2 & T & T & T & q4 \\\hline\end{tabular}
Q. Construct the truth table.\begin{tabular}{|c|c|c|c|c|}\hlinep & q & r & (r∧q)∨p & (q∨p)∧r \\\hlineT & T & T & T & T \\\hlineT & T & q2 & T & q4 \\\hlineT & q2 & T & q2 & q4 \\\hlineT & q2 & q2 & q2 & q4 \\\hlineq2 & T & T & T & q4 \\\hline\end{tabular}
Fill Given Values: First, let's fill in the given values for p, q, and r in the first three columns.Now, calculate the value of (r∧q) for each row. This is the logical AND of r and q.T∧T=T, T∧T=T, T∧F=F, T∧F=F, q0, q0.
Calculate (r∧q): Next, calculate the value of (r∧q)∨p for each row. This is the logical OR of the previous result and p.T∨T=T, T∨T=T, F∨T=T, F∨T=T, F∨F=F, F∨F=F.
Calculate (r∧q)∨p: Then, calculate the value of (q∨p) for each row. This is the logical OR of q and p.T∨T=T, T∨T=T, F∨T=T, F∨T=T, T∨F=T, T∨F=T.
Calculate (q∨p): Finally, calculate the value of (q∨p)∧r for each row. This is the logical AND of the previous result and r.T∧T=T, T∧F=F, T∧T=T, T∧F=F, T∧T=T, T∧F=F.
Calculate (q∨p)∧r: Fill in the truth table with the calculated values for (r∧q)∨p and (q∨p)∧r.Check for any math errors in the calculations and the final truth table.
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