Questions: Construct the truth table for the compound statement (p ∧ ~q) ∨ ~r. Fill in the empty values of the truth table for the final compound statement. Truth Table p q (p ∧ ~q) ∨ r --------------------- T T T 7 T T F ✓ T F T ✓ T F F ✓ F T T ✓ F T F 7 F F ✓ F F ✓

Construct the truth table for the compound statement (p ∧ ~q) ∨ ~r. Fill in the empty values of the truth table for the final compound statement. Truth Table p q (p ∧ ~q) ∨ r --------------------- T T T 7 T T F ✓ T F T ✓ T F F ✓ F T T ✓ F T F 7 F F ✓ F F ✓
Transcript text: Construct the truth table for the compound statement $(p \wedge \sim q) \vee \sim r$. Fill in the empty values of the truth table for the final compound statement. \begin{tabular}{|c|c|c|c|c|c|c|} \hline \multicolumn{7}{|c|}{Truth Tablo} \\ \hline p & q & & & (p^ q) & V & r \\ \hline T & T & & T & & 7 & \\ \hline T & T & & F & & $\checkmark$ & \\ \hline T & F & & T & & $\checkmark$ & \\ \hline T & F & & F & & $\checkmark$ & \\ \hline F & T & & T & & $\checkmark$ & \\ \hline F & T & & F & & 7 & \\ \hline F & F & & & & $\checkmark$ & \\ \hline F & F & & & & $\checkmark$ & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Identify Variables and Operators

Given compound statement: (p and not q) or not r

Variables identified: p, q, r

Step 2: Determine Table Size

Number of unique variables: 3 Total rows in the truth table: 8

Step 3: Assign Truth Values

| p | q | r | Result | | - | - | - | - | | F | F | F | T | | F | F | T | F | | F | T | F | T | | F | T | T | F | | T | F | F | T | | T | F | T | T | | T | T | F | T | | T | T | T | F |

Final Answer:

The complete truth table for the given compound statement is shown above.

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