Question

a law of deductive reasoning that states that if a conditional statement is true and its hypothesis is true, then the conclusion will also be true
○ valid argument
○ conjunction
○ law of detachment
○ law of syllogism

1. what words match this description?

an argument that uses logic in the form of definitions, properties, and previously proved principles to show that a conclusion is true
○ conjunction
○ valid argument
○ argument
○ proof

Explanation:

First Question:

• A valid argument is a general term for a logically sound argument, not specific to this rule.
• Conjunction is a logical operation (like "and"), not related.
• Law of Detachment (also Modus Ponens) states that if \( p \to q \) is true and \( p \) is true, then \( q \) is true, matching the description.
• Law of Syllogism deals with chaining conditionals (\( p \to q \), \( q \to r \) implies \( p \to r \)), not this.

• Conjunction is a logical connective, not an argument type for proving.
• Valid argument is an argument with a valid form, not the process of proving.
• Argument is a general term for a set of statements, not the proof.
• Proof is an argument using logic, definitions, properties, and proven principles to show a conclusion is true, matching the description.

Answer:

C. Law of Detachment

Second Question: