Given the argument: J ⊃ (E • Q) / ∼ Q ⊃ L / (E ∨ M) ⊃ (L ∨ ∼ Q) / M ∨ J // L
This argument is:
A) Valid.
B) Invalid.
C) Sound.
D) Cogent.
E) Uncogent.

Question

Quizplus · Accepted Answer

The argument is valid because if we assume the premises to be true, the conclusion logically follows. We can use the method of conditional proof to demonstrate the validity of the argument:

1. J ⊃ (E • Q)
2. ∼ Q ⊃ L
3. (E ∨ M) ⊃ (L ∨ ∼ Q)
4. M ∨ J // L
5. Assume ¬L for conditional proof
6. Therefore, ¬(E ∨ M) (From 3)
7. Therefore, (∼ E ∧ ∼ M) (De Morgan's Law for 6)
8. Therefore, ∼ M (From 7)
9. Therefore, J (From 4 and 8 by Disjunctive Syllogism)
10. Therefore, E • Q (From 1 and 9 by Modus Ponens)
11. Therefore, Q (From 10 by Simplification)
12. Therefore, L (From 2 and 11 by Modus Ponens)
13. Therefore, ¬¬L (From 5 by reductio ad absurdum)
14. Therefore, L (From 13 by Double Negation).

Since we were able to arrive at the conclusion L through a valid logical sequence, the argument is considered valid.

Given the Argument: J ⊃ (E • Q) / ∼