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

To identify the valid reasoning structure or invalid reasoning error for each symbolic argument, we need to analyze the logical form of each argument.<br /><br />**Argument #1:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \( p \)<br />- Conclusion: \( a \)<br /><br />This argument does not follow a standard logical form because the conclusion \( a \) is unrelated to the premises. Therefore, this represents an **invalid reasoning error** known as "irrelevant conclusion" or "non sequitur."<br /><br />**Argument #2:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \( p \)<br />- Conclusion: \( \sim q \)<br /><br />This argument is invalid because it contradicts itself. If \( p \rightarrow q \) and \( p \) are true, then \( q \) must be true, not \( \sim q \). This represents an **invalid reasoning error** known as "denying the antecedent."<br /><br />**Argument #3:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \( q \)<br />- Conclusion: \( \therefore p \)<br /><br />This argument is invalid because it assumes that if \( q \) is true, then \( p \) must also be true, which is not necessarily the case. This represents an **invalid reasoning error** known as "affirming the consequent."<br /><br />**Argument #4:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \( q \)<br />- Conclusion: \( \sim p \)<br /><br />This argument is invalid because it incorrectly concludes \( \sim p \) from \( q \). The presence of \( q \) does not imply \( \sim p \). This represents an **invalid reasoning error** similar to "affirming the consequent."<br /><br />In summary:<br />- Argument #1: Invalid reasoning error (irrelevant conclusion).<br />- Argument #2: Invalid reasoning error (denying the antecedent).<br />- Argument #3: Invalid reasoning error (affirming the consequent).<br />- Argument #4: Invalid reasoning error (similar to affirming the consequent).