Given the argument: M ⊃ J / ∼ J ⊃ R // (M ∨ ∼ R) ⊃ J
This argument is:
A) Invalid; fails in 3rd line.
B) Invalid; fails in 2nd line.
C) Invalid; fails in 4th line.
D) Invalid; fails in 1st line.
E) Valid.

Question

Quizplus · Accepted Answer

The argument is valid. We can use conditional proof to demonstrate this. First, we assume (M ∨ ∼ R) and aim to show J. If M is true, then by the first premise M ⊃ J, we have J. If ∼ R is true, then by the second premise ∼ J ⊃ R, we have ∼ J. But this contradicts our assumption of (M ∨ ∼ R). Therefore, ∼ R must be false and R must be true. Now we can use the second premise ∼ J ⊃ R to conclude ∼ J is false, and therefore J must be true. Thus, we have shown that (M ∨ ∼ R) ⊃ J is true, and the argument is valid.

Given the Argument: M ⊃ J / ∼ J ⊃