Identify what you can properly conclude from the given premises:P: A → MP: not X → JP: X → not MC: ?

jakennedy January 15, 2022

Hi,

I’d be happy to explain how to do this sort of question.

This is an argument completion drill. They are an example of what may occur on a Must be True question when they incorporate conditional logic. Your goal is to find inferences using the transitive property.

For example, this one says:

P: A? M
P: not X ? J
P: X ? not M

Let’s begin with the first premise:

A ? M

In order to find inferences, we have to look at the remaining premises and find a common element, A or M. Premise two has none of those elements, so we would skip it for now. Premise three almost has an M, but it says not M. Thus, we have to take the contrapositive of premise 3:

M ? not X

Now that we have M in two statements, we can combine them:

A ? M ? not X

Upon adding premise three, we would revisit premise two. We now have not X in our chain and in premise two, so we can combine them as well:

A ? M ? not X ? J

and its contrapositive:

not J ? X ? not M ? not A

On a real must be true question, the answer could be any part of these chains. For example, the answer could say:

“if M then J”
“if not J then not M”

More often than not, however, the answer will include the endpoints:

"if A then J”
“if not J then not A”

The argument completion drill will always use the endpoints as the answer, so this would be:

A ? J or not J ? not A.

On real questions, check the endpoints first, but remember that there are other potential correct answers as well.

Hope this helps!

Jean December 6, 2022

If one answer was [ A-> J] that would be correct, right? and the answer [not J -> not A] is correct because of the contrapositive? Or am I missing something?

Emil-Kunkin December 11, 2022

You are indeed correct, those two statements are equivalent, so either would be correct here