Just a quick question in the middle of some study

[ManhattanPrepLSAT1]

I may regret this post if it's responded to after I figure the answer I'm looking for but here's to community.

In if then statement of :

If A is not in placement 3 then C is in a higher numbered placement than B.
The order follows 1 < 2


The notation should follow like this:

if (NOT A3) -> B< C

It's contrapositive would then be, according to my study aid:

If C< B -> A3

Why is C possibly equal to but not just less than B, in the contrapositive?

Thanks for any help!

[ManhattanPrepLSAT1]

That is correct.

One way to think about it is --

If the original conditional is " If X, then Y," the contrapositive, in words is -- "Whatever is not Y must mean no X."

The original condition is - A3 -> C > B.

When is C> B NOT true? When C < B or (when the game allows) when C = B. Therefore, you must consider both of these situations in coming up with the contrapositive.

Mathematically speaking, imagine there was a rule "Only those who score over 100 points win the game." Who would NOT win? Either those who score less than 100, or exactly 100. Hope that helps!

[ManhattanPrepLSAT1]

Yes, that makes perfect sense.

Sorry to the board that this thread ended up in the do not post section.