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!
Weird Constraint Wording Forum
- incompetentia
- Posts: 2277
- Joined: Thu Sep 30, 2010 2:57 pm
Re: Weird Constraint Wording
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.
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.
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- Posts: 71
- Joined: Sat Jan 15, 2011 2:03 pm
Re: Weird Constraint Wording
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?
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?
- incompetentia
- Posts: 2277
- Joined: Thu Sep 30, 2010 2:57 pm
Re: Weird Constraint Wording
I think the contrapositive would be something like
If Q or R is not first or last, then U would be in that position.
If Q or R is not first or last, then U would be in that position.
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