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

Question

Quizplus · Accepted Answer

This argument is valid. 
To show validity, we can use a proof by contradiction. Assume that Q is true and C is false. From Q ⊃ (A ∨ M), we know that either A or M is true. If A is true, then from A ⊃ (W ∨ C), we know that either W or C is true. But since we assumed that C is false, it must be the case that W is true. From ~(W ∨ E), we know that both W and E are false. Therefore, we have a contradiction: we initially assumed that Q is true, but we ended up with W being true and ~(W ∨ E) being true as well. Hence, we must reject our assumption that C is false, and accept that Q ⊃ C.

Given the Argument: Q ⊃ (A ∨ M) / a ⊃