Conditional Rules - LG

[Dunlap29]

I have a basic question:

If S - P then M - S = M - S - P
S - M then P - S = P - S - M

What is the logic for the second line? Where does it come from?

[Dunlap29]

Just to clarify:

The rule stated : "If S is before P then M is before S"

I found someone had diagrammed it this way:

S-P then M-S M-S-P
S-M then P-S P-S-M

I'm trying to understand where the logic for the second line comes from?

Thanks, Steve

[Dunlap29]

I got it. It is one or the other.

[Adam Tyson]

Not quite, Dunlap29, but close! The reason for that second diagram is that it is the contrapositive of the first one. If S is before M, then the Necessary Condition in the original rule is not met, and that means the Sufficient Condition cannot occur. Assuming this is a game with no ties allowed, if S cannot be before P then it must be after it.

The reason I say it's not quite a "one or the other" scenario is that there appears to be a third alternative here. What if the conditional rule is never triggered? Could we perhaps have a situation where M and P are both before S? The Sufficient Condition of S before P doesn't occur, but the Necessary Condition of M before S does occur. The rule in its original form is not activated due to the absence of the Sufficient Condition, but the contrapositive also is not activated due to the Necessary Condition occurring. Behold, a third option appears!

Conditional rules can be tricky like that. Watch for three things, usually:
1) Sufficient Condition occurs and Necessary Condition occurs
2) Necessary Condition does not occur and Sufficient Condition does not occur
3) Necessary Condition occurs, but Sufficient Condition does not. The rule is not triggered. This is the one many students will overlook, and so you can bet that LSAC will capitalize on that and set up situations where an unwary student will reject a perfectly good answer or select one that does not have to be true.

Be careful out there!