Weird Constraint Wording

Bigsby
Posts: 71
Joined: Sat Jan 15, 2011 2:03 pm

Weird Constraint Wording

Postby Bigsby » Sun Jun 05, 2011 12:37 pm

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!

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incompetentia
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Re: Weird Constraint Wording

Postby incompetentia » Sun Jun 05, 2011 12:49 pm

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.

Bigsby
Posts: 71
Joined: Sat Jan 15, 2011 2:03 pm

Re: Weird Constraint Wording

Postby Bigsby » Sun Jun 05, 2011 3:03 pm

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?

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incompetentia
Posts: 2307
Joined: Thu Sep 30, 2010 2:57 pm

Re: Weird Constraint Wording

Postby incompetentia » Sun Jun 05, 2011 3:11 pm

I think the contrapositive would be something like

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




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