Question

For J ⊃ (K⊃L) / K ⊃ (J ⊃ L) // (J v K) ⊃ L, what can be concluded?

A) K ⊃ L
B) J ⊃ L
C) J v K
D) J ⊃ (K ⊃ L)

Answer 1

The given argument is shown to be valid using the method of conditional proofs, also known as the conditional derivation rule. Therefore, the correct answer is D) J ⊃ (K ⊃ L).

Step-by-step explanation:

The given argument is shown to be valid using the method of conditional proofs, also known as the conditional derivation rule.

1. Assume the premise J ⊃ (K⊃L) is true. (1st premise)
2. Apply the rule of Implication (→ Introduction) to conclude K ⊃ (J ⊃ L) from J ⊃ (K⊃L). (3rd premise)
3. Introduce the assumption J v K. (2nd premise)
4. Apply the rule of Implication (→ Introduction) to conclude (J v K) ⊃ L from K ⊃ (J ⊃ L) and J v K.
5. Since we’ve arrived at L from the assumption (J v K), we can conclude (J v K) ⊃ L.

Therefore, the correct answer is D) J ⊃ (K ⊃ L).