Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Construct the truth table.





p

q

r

(r^^q)vv p

(q vv p)^^r



T

T

T

T

T



T

T

F

T

◻



T

F

T

F

◻



T

F

F

F

◻



F

T

T

T

◻

Construct the truth table.\newline\begin{tabular}{|c|c|c|c|c|}\newline\hlinep p & q q & r r & (rq)p (r \wedge q) \vee p & (qp)r (q \vee p) \wedge r \\\newline\hlineT T & T T & T T & T T & T T \\\newline\hlineT T & T T & q q 22 & T T & q q 44 \\\newline\hlineT T & q q 22 & T T & q q 22 & q q 44 \\\newline\hlineT T & q q 22 & q q 22 & q q 22 & q q 44 \\\newline\hlineq q 22 & T T & T T & T T & q q 44 \\\newline\hline\newline\end{tabular}

Full solution

Q. Construct the truth table.\newline\begin{tabular}{|c|c|c|c|c|}\newline\hlinep p & q q & r r & (rq)p (r \wedge q) \vee p & (qp)r (q \vee p) \wedge r \\\newline\hlineT T & T T & T T & T T & T T \\\newline\hlineT T & T T & q q 22 & T T & q q 44 \\\newline\hlineT T & q q 22 & T T & q q 22 & q q 44 \\\newline\hlineT T & q q 22 & q q 22 & q q 22 & q q 44 \\\newline\hlineq q 22 & T T & T T & T T & q q 44 \\\newline\hline\newline\end{tabular}
  1. Fill Given Values: First, let's fill in the given values for pp, qq, and rr in the first three columns.\newline\newlineNow, calculate the value of (rq)(r \land q) for each row. This is the logical AND of rr and qq.\newlineTT=TT \land T = T, TT=TT \land T = T, TF=FT \land F = F, TF=FT \land F = F, qq00, qq00.
  2. Calculate (rq)(r \land q): Next, calculate the value of (rq)p(r \land q) \lor p for each row. This is the logical OR of the previous result and pp.TT=TT \lor T = T, TT=TT \lor T = T, FT=TF \lor T = T, FT=TF \lor T = T, FF=FF \lor F = F, FF=FF \lor F = F.
  3. Calculate (rq)p(r \land q) \lor p: Then, calculate the value of (qp)(q \lor p) for each row. This is the logical OR of qq and pp.TT=TT \lor T = T, TT=TT \lor T = T, FT=TF \lor T = T, FT=TF \lor T = T, TF=TT \lor F = T, TF=TT \lor F = T.
  4. Calculate (qp)(q \lor p): Finally, calculate the value of (qp)r(q \lor p) \land r for each row. This is the logical AND of the previous result and rr.TT=TT \land T = T, TF=FT \land F = F, TT=TT \land T = T, TF=FT \land F = F, TT=TT \land T = T, TF=FT \land F = F.
  5. Calculate (qp)r(q \lor p) \land r: Fill in the truth table with the calculated values for (rq)p(r \land q) \lor p and (qp)r(q \lor p) \land r.\newline\newlineCheck for any math errors in the calculations and the final truth table.

More problems from Find derivatives using the product rule I