Question

Use the first four rules of inference (MP, MT, HS, DS) to derive the conclusion of the following symbolized argument.

J ⊃ (K ⊃ L)/L ∨ J/∼L//∼K

Answer 1

By applying the Hypothetical Syllogism and Modus Tollens, we get the desired conclusion that the symbolized argument is ∼K.

Step-by-step explanation:

To derive the conclusion of the given argument using the first four rules of inference (MP, MT, HS, DS), we need to analyze the premises and apply the appropriate rule to reach the conclusion.

Let's break it down:

1. Premise 1: J ⊃ (K ⊃ L)
2. Premise 2: L ∨ J
3. Premise 3: ∼L
4. Using the Hypothetical Syllogism (HS) rule, we can combine Premise 1 and Premise 2 to derive K ⊃ L: J ⊃ (K ⊃ L), L ∨ J ∴ K ⊃ L
5. Now, applying Modus Tollens (MT) with Premise 3 and the derived K ⊃ L from the previous step, we get ∼K: ∼L, K ⊃ L ∴ ∼K

Therefore, the conclusion of the argument is ∼K.