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

Question

Quizplus · Accepted Answer

The argument is invalid. One way to see this is to construct a counterexample where all the premises are true, but the conclusion is false. Let's assume that C is true, which means that M is false. Given this, the first premise (C ⊃ ∼ M) is true. We can also assume that I is true, and therefore ∼ H is true, making the second premise (I ⊃ ∼ H) true. Now we need to consider the third premise: (N • I) ∨ (G • C). Since we know that I is true, let's assume that N is true, which means that (N • I) is true. Therefore, we only need to consider the truth value of (G • C). But we already know that C is true and M is false, so we cannot assume that G is true, since G • C would then be false. Therefore, the third premise is false, and the argument is invalid. We do not need to consider the last two premises or the conclusion, since the argument is already invalid.

Given the Argument: C ⊃ ∼ M / I ⊃