Conditional Reasoning

cmapoma

This might be something really basic to be discussing at this time for someone looking to sit for the LSATs in December, but I gotta ask

How would you guys diagram this conditional sentence: "Unless they find an eye-witness and put the defendant on the stand, they will lose the case."

Please explain. Thanks.

Daniel.Sieradzki

Never feel that anything is basic. This is actually kind of tricky because there is a conjunction in the conditional.

This is a group 3 conditional. It can be solved by negating one of the two parts of the conditional and making that particular part the sufficient condition.

Here are the two parts (this is hard because one of the parts is actually two things):
Part 1: EW = Eye Witness & D = Defendant
Part 2: L = Lose Case

Thus, you can either negate (EW & D) and make that the sufficient condition or negate L and make that the sufficient condition.

Way 1: ~L -> (EW & D)

or

Way 2: ~(EW & D) -> L

Either way is correct.

It is also worth noting that Way 2 can be also written as (~EW or ~D) -> L. This is because ~(EW & D) means not both EW and D. In other words, at least ~EW or ~D. This is known as De Morgan's Law in logic.

Let me know if you have any questions. Good luck in December!

MrSamIam

@Daniel.Sieradzki Covered it well. One thing that I do want to mention, which Daniel implied, is that it doesn't matter which of the conditions you choose to be the sufficient or necessary - so long as you negate whichever you've chosen to be the sufficient.

MsM1998_

Testing my knowledge (correct me if im wrong)
~ L -> (EW & D) can also be split since it's an "and " in the necessary condition. In this case it would be ~L -> EW and ~L -> D, same can be done for the other version too, I think. Can someone confirm this for me? (im also trying to learn)

M.Yanka106

MrYC, you are correct about the split

dcdcdcdcdc

Good call on taking it a step further and splitting. Helps think about the statement:

if you don't find a witness, then you lose
if you the defendant does not take the stand, then you lose
---
if you win, then you found a witness and the defendant took the stand

I could see that first part of splitting the sufficient or condition as really helping solve an LR question, because it shows the minimum condition that leads to a loss.