Solution Found!
1. M (K L) 2. (L N ) J / M (K J )
Chapter 7, Problem 11(choose chapter or problem)
Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.
1. \(M \supset(K \supset L)\)
2. \((L \vee N) \supset J \quad \text { / } M \supset(K \supset J)\)
Questions & Answers
QUESTION:
Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.
1. \(M \supset(K \supset L)\)
2. \((L \vee N) \supset J \quad \text { / } M \supset(K \supset J)\)
ANSWER:Step 1 of 3
The conclusion \(M \supset \left( {K \supset J} \right)\) is derived as shown below.
Since the conclusion has 2 conditional statements, then assume two conditional proofs:
Start with Conditional Proof.
Assume the conditional proof (ACP) as shown below:
\(3.M\;\;\;\;\;\;\;\;\;\;\;\;\;ACP\)
Assuming second Conditional Proof, using assuming conditional proof (ACP) as shown below:
\(4.K\;\;\;\;\;\;\;\;\;\;\;\;\;\;ACP\)
Solve the premises1 and 3 to eliminate the terms using modus ponens:
\(5.K \supset L\;\;\;\;\;\;\;\;\;1,3,MP\)