For each symbolic argument below, identify the valid reasoning structure or invalid reasoning error it represents. Argument #1: - Premise: parrow q Premise: p Conclusion: q Logical form: square Argument #2: - Premise: parrow q Premise: -p =p Conclusion: -q Logical form: Select an answer square Argument #3: Premise: parrow q Premise: a Conclusion: ..p Logical form: square Argument #4: - Premise: parrow q Premise:- a Conclusion: -p Logical form: square

To identify the valid reasoning structure or invalid reasoning error for each argument, let's analyze them one by one:<br /><br />**Argument #1:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \( p \)<br />- Conclusion: \( q \)<br /><br />This argument follows the logical form known as **Modus Ponens**, which is a valid form of reasoning. If \( p \) implies \( q \) and \( p \) is true, then \( q \) must also be true.<br /><br />**Argument #2:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \(\sim p\)<br />- Conclusion: \(\sim q\)<br /><br />This argument represents an invalid reasoning error known as **Denying the Antecedent**. Just because \( p \) is false does not necessarily mean that \( q \) is false.<br /><br />**Argument #3:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \( q \)<br />- Conclusion: \( p \)<br /><br />This argument represents an invalid reasoning error known as **Affirming the Consequent**. Just because \( q \) is true does not necessarily mean that \( p \) is true.<br /><br />**Argument #4:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \(\sim q\)<br />- Conclusion: \(\sim p\)<br /><br />This argument follows the logical form known as **Modus Tollens**, which is a valid form of reasoning. If \( p \) implies \( q \) and \( q \) is false, then \( p \) must also be false.<br /><br />In summary:<br />- Argument #1: Modus Ponens (valid)<br />- Argument #2: Denying the Antecedent (invalid)<br />- Argument #3: Affirming the Consequent (invalid)<br />- Argument #4: Modus Tollens (valid)