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I was doing a 'Rule Equivalency' exercise today and here was the sample they gave:

Five people—Q, R, S, T, and U—finish a race in order.

S finishes third.
T finishes immediately before or immediately after S.
Q finishes at some point before R

The question is what rule can you replace so that we still get T is immediately before or after S.

They said one constraint possible that would fulfill this is:
If not U, only Q or R can be first or last.

I can see this being diagrammed as:

only Q or R is first or last> U is not first or last

contrapositive:
U is first or last> ???

is it Q or R is not first or last?

if so, doesn't that go against the constraint and allow T to be last?

Thanks!

This wording is dubious as hell and would never appear on a real test, in my opinion.

The reason I think this works is that what it's saying is that only U, Q, or R can go in the first and last positions.


Since we have given that S is third, and T can't be first or last, this still constrains T to second or fourth.

Agreed with the dubious wording. I see how the statement, non-contraposed, limits T with S but I don't exactly know what the contrapositive is to this rule. If it were contraposed as I worded it, it does not constrain T with S and in fact T can be last.

Rule:
Only Q or R is first or last> U is not first or last

contrapositive:
U is first or last> ???

is it "Q or R is not first or last"?

in that case we can have "U Q S R T"

right?

I think the contrapositive would be something like

If Q or R is not first or last, then U would be in that position.