(1) Given: \( \begin{array}{l}p \vee q \\ r \rightarrow \sim q \\ r\end{array} \)
Prove: \( p \)

Answer

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Answer

4. Simplify double negation and apply Modus Ponens: \(p \)

Steps

Step 1 ：1. Apply Modus Tollens on second and third given expressions: \(\sim r \vee \sim \sim q \)

Step 2 ：2. Simplify double negation: \(\sim r \vee q \)

Step 3 ：3. Apply Modus Tollens on first given expression and result from step 2: \(\sim p \rightarrow \sim \sim r \)

Step 4 ：4. Simplify double negation and apply Modus Ponens: \(p \)