Question

With reference to the formal proof of validity of the following argument, state the correct order of rules employed.
1. \( P \cdot Q \)
2. \( ( P \vee R ) \supset S / \therefore P \cdot S \)
3. P
4. \( P \vee R \)
5. S
6. \( P \cdot S \)
A. Conjunction
B. Modus Ponens
C. Addition
D. Simplification
Choose the correct answer from the options given below:

• A. A, B, C, D
• B. B, A, D, C
• C. D, C, B, A
• D. C, B, A, D

Hint:

In formal proofs, remember to apply Simplification to break down conjunctions, Addition to introduce disjunctions, Modus Ponens to apply conditionals, and Conjunction to combine statements.

Answer 1

The Correct Option is C

Step 1: Understanding the formal proof rules.
The argument follows a set of logical rules to prove the conclusion \( P \cdot S \) from the given premises. We analyze each step in the argument: - D. Simplification: The first step involves simplifying the conjunction \( P \cdot Q \) to \( P \), which uses the rule of Simplification. - C. Addition: In the second step, \( P \) is added to \( P \vee R \), following the rule of Addition (since \( P \) alone implies \( P \vee R \)). - B. Modus Ponens: The third step uses Modus Ponens with the premise \( (P \vee R) \supset S \) and \( P \vee R \) to deduce \( S \). - A. Conjunction: Finally, we combine \( P \) and \( S \) to form the conclusion \( P \cdot S \), applying the rule of Conjunction.
Step 2: Conclusion. The correct order of rules is D, C, B, A.
Final Answer: \[ \boxed{\text{The correct answer is 3. D, C, B, A.}} \]