3.2.4.1: Exercises
- Page ID
- 93135
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Truth Tables
- Translate each statement from symbolic notation into English sentences. Let A represent “Elvis is alive” and let G represent “Elvis gained weight”.
- \(A \vee G\)
- \(\sim(A \wedge G)\)
- For questions 2 - 3, use the statements A and G from the previous problem and let statement P represent "Elvis is in Vegas". Translate each statement from symbolic notation into English sentences then create a truth table for each statement.
- \(A \wedge \sim G\)
- \(\sim(\sim A \vee G)\)
- Complete the truth table for the exclusive or.
\(\begin{array}{|c|c|c|} \hline A & B & A \vee B \\ \hline \mathrm{T} & \mathrm{T} & \\ \hline \mathrm{T} & \mathrm{F} & \\ \hline \mathrm{F} & \mathrm{T} & \\ \hline \mathrm{F} & \mathrm{F} & \\ \hline \end{array}\)
- Complete the truth table for \((A \vee B) \wedge \sim(A \wedge B)\).
\(\begin{array}{|c|c|c|c|c|c|} \hline A & B & A \vee B & A \wedge B & \sim(A \wedge B) & (A \vee B) \wedge \sim(A \wedge B) \\ \hline \mathrm{T} & \mathrm{T} & & & & \\ \hline \mathrm{T} & \mathrm{F} & & & & \\ \hline \mathrm{F} & \mathrm{T} & & & & \\ \hline \mathrm{F} & \mathrm{F} & & & & \\ \hline \end{array}\)
- Compare your answers for questions 3 and 4. Can you explain the similarities?