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

Question

Quizplus · Accepted Answer

The premises are (A • B) ∨ (C • D), E ⊃ ∼ B, and F ⊃ ∼ D. 
Using the first premise, we can separate it into two cases: A • B or C • D. 
Assume E is true. From E ⊃ ∼ B, we can conclude that ∼ B is true. Similarly, assume F is true. From F ⊃ ∼ D, we can conclude that ∼ D is true. 
If A • B is true, then from ∼ B, we can conclude that ∼ A is true. But we cannot make any conclusion about C. 
If C • D is true, then from ∼ D, we can conclude that ∼ C is true. But we cannot make any conclusion about A. 
Therefore, we cannot conclude that A • C necessarily follows from the premises and conclusion (E ∨ F) given, making the argument invalid.

Given the Argument: (A • B) ∨ (C • D)