Word Count : 272

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We are given a compound logical implication to prove: $$ (p \rightarrow q) \wedge (\sim q \rightarrow r) \wedge r \wedge \sim q \Rightarrow \sim p $$ --- ### Step-by-step Proof (Using Truth Table or Logical Equivalences): We'll proceed using logical equivalences to simplify step-by-step. --- ### Step 1: Understand each component: We are given: 1. $p \rightarrow q$ 2. $\sim q \rightarrow r$ 3. $r$ 4. $\sim ________ ________ ____ _____ ______ __________ ____ ___ ________ ____ __________.
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