For each symbolic argument below,identify the valid reasoning structure or inv represents. Argument #1: Premise: parrow q Premise: p p Conclusion: q Logical form V Select an answer Transitive Property Law of Detachment Fallacy of the Inverse Fallacy of the Converse Premi Law of Contraposition Premise: -D =p Conclusion: -q Argument #2 Logical form: Select an answer Argument #3: Premise: parrow q Premise: a q Conclusion: Logical form: Select an answer Argument #4: Premise: parrow q Premise: - a =q Conclusion: -p Logical form: Select an answer

Let's analyze each argument and identify the logical reasoning structure it represents:<br /><br />**Argument #1:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \( p \)<br />- Conclusion: \( q \)<br /><br />This is an example of the **Law of Detachment** (also known as Modus Ponens). The Law of Detachment states that if a conditional statement (\( p \rightarrow q \)) is true and its antecedent (\( p \)) is true, then the consequent (\( q \)) must also be true.<br /><br />**Argument #2:**<br />- Premise: \( \sim p \)<br />- Conclusion: \( \sim q \)<br /><br />This argument seems to be missing some context or additional premises. However, based on the given information, this resembles the **Fallacy of the Inverse**. The Fallacy of the Inverse occurs when one assumes that if \( p \rightarrow q \) is true, then \( \sim p \rightarrow \sim q \) must also be true, which is not a valid form of reasoning.<br /><br />**Argument #3:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \( q \)<br />- Conclusion: \( \therefore p \)<br /><br />This is an example of the **Fallacy of the Converse**. The Fallacy of the Converse occurs when one assumes that if \( p \rightarrow q \) is true, then \( q \rightarrow p \) must also be true, which is not necessarily valid.<br /><br />**Argument #4:**<br />- Premise: \( p \rightarrow q \)<br />- Premise: \( \sim q \)<br />- Conclusion: \( \sim p \)<br /><br />This is an example of the **Law of Contraposition**. The Law of Contraposition states that a conditional statement (\( p \rightarrow q \)) is logically equivalent to its contrapositive (\( \sim q \rightarrow \sim p \)). If the contrapositive is true, then the original statement is also true.<br /><br />In summary:<br />- Argument #1: Law of Detachment<br />- Argument #2: Fallacy of the Inverse<br />- Argument #3: Fallacy of the Converse<br />- Argument #4: Law of Contraposition