1. **Problem:** Elephants have cells in their bodies, and all cells have DNA. Therefore, what can we conclude? 2. **Problem:** All horses have manes. The Appaloosa is a horse; therefore, do Appaloosas have manes? --- ### Step 1: Understand the logical forms - Affirm the Antecedent (Modus Ponens): If $p \to q$ and $p$ is true, then $q$ is true. - Deny the Consequent (Modus Tollens): If $p \to q$ and $\neg q$ is true, then $\neg p$ is true. - Affirm the Consequent: If $p \to q$ and $q$ is true, it does NOT necessarily mean $p$ is true. - Deny the Antecedent: If $p \to q$ and $\neg p$ is true, it does NOT necessarily mean $\neg q$ is true. --- ### Step 2: Apply to problem 1 - Given: Elephants have cells ($p$), all cells have DNA ($p \to q$). - By Affirming the Antecedent: Since elephants have cells ($p$), and all cells have DNA ($p \to q$), then elephants have DNA ($q$). ### Step 3: Apply to problem 2 - Given: All horses have manes ($p \to q$), Appaloosa is a horse ($p$). - By Affirming the Antecedent: Since Appaloosa is a horse ($p$), and all horses have manes ($p \to q$), then Appaloosas have manes ($q$). --- ### Final answers: 1. Elephants have DNA. 2. Appaloosas have manes.