(1) Given: $\begin{array}{l} p \lor q \\ r \to\sim q \\ r \end{array}$
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: $\sim r \lor \sim\sim q$

Step 2 ：2. Simplify double negation: $\sim r \lor q$

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

Step 4 ：4. Simplify double negation and apply Modus Ponens: $p$