(∼C ⊃ ∼J) • (P ⊃ L)
A) CD-valid.
B) Invalid.
C) DD-valid.
D) MT-valid.
E) CD-invalid.

Question

(∼C ⊃ ∼J) • (P ⊃ L) 
A) CD-valid. 
B) Invalid. 
C) DD-valid. 
D) MT-valid. 
E) CD-invalid.

Quizplus · Accepted Answer

The argument can be proven by using a valid argument form called Denying the Antecedent (DA). The argument can be reformulated into the following two premises: 
1) If not C, then not J. (equivalent to ∼C ⊃ ∼J) 
2) If P, then L. (equivalent to P ⊃ L)

To use DA, assume the antecedent of the first premise (~C) and derive a contradiction. Then, we can conclude the negation of the consequent of the first premise (∼J). Finally, using modus ponens with the second premise, we can infer L.

Here is a formal proof:
1. ~C ⊃ ~J     Premise 
2. P ⊃ L       Premise
3. ~C          Assumption 
4. ~J          Modus tollens 1,3 
5. P           Assumption 
6. L           Modus ponens 2,5 
7. C ⊃ L       Conditional proof 3-6 
8. ~(C ⊃ L)    Negation introduction 7 
9. DD           Disjunctive syllogism 8 
Therefore, the argument is DD-valid.