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Annet on January 19 at 10:20PM

Missing premises

I have come across an issue with these because I am underuse where the "not" is supposed to be. Take the following example: P1: A -> Not B P2: ? C: B -> C The correct answer for premise 2 is: Not A -> C with the Contrastive being Not C -> A But I put down the following: A -> Not C with the contrapositive being C -> Not A I want to know how to differentiate between what variable the not should be put or does this not matter?

1 Reply

on January 20 at 12:05AM

Hello @annetr0712,

It does matter which variable is negated, because the answer that you first provided does not lead to the conclusion. Let's test it.

P1: A - > not B
P2: A - > not C or C - > not A
C: B - > C

Ok, the conclusion gives us B. From premise 1, we get not A. This is what we need to use to get to the conclusion. With the premise 2 that you provided, not A does not lead to the conclusion. It does not guarantee C.

Here is how we need to approach this problem.

P1: A - > not B
P2: ?
C: B - > C

The conclusion gives us B. From premise 1, we get not A. How can we say that not A leads to C? We can simply write:

not A - > C
or
not C - > A

With the correct answer, not A is sufficient for C. This means that it guarantees the conclusion is properly drawn.

With your previous answer, not A is necessary for C. It does not guarantee the conclusion.