Diagram

[sethgrant]

Can someone please walk me through the setup of this game. Not sure why but I literally froze when I was taking this as a PT! I had trouble diagramming the rules as well...

Also if you can think of any similar games I would love to work on them!

[aileenann]

Thanks for your question. I am attaching my set-up. Let me know what you think and whether you need help working through any of the questions! As with many closed assignment games, I did not see many inferences - do you see any?

[dan]

Here's the completed diagram.



And attached is a full solution that Matt wrote up.

[nzheng]

Hi, I also had a problem with this game, and I think it came down to interpreting the 1st conditional clue incorrectly, as I i was unable to infer that it was a biconditional. I feel like I need further clarification on the whole "if BUT only if" phrase.
Why is this not the same as "only if"? And for that matter, would the phrase "if AND only if" be a biconditional as well? thanks in advance for the reply.

[noah]

"If and only if" and "If but only if" are both bi-conditionals. Consider them as statements that you can break into two parts:

Tom is accepted if and only if he writes a song

1. Tom is accepted if he writes a song. AND
2. Tom is accepted only if he writes a song.

"Only if" sets up the necessary side of a conditional statement.

Does that clear it up?

[rmoncel]

Hi there:

Thanks for the diagrams and answers. I set this up as an open assignment game with the people (G, H, J, M) as the base. I got all answers right but it took me 9 minutes to complete, as opposed to less than 6 when, after consulting the forum, I set this up as a closed assignment game with the pieces of furniture (r, s, t) as the base.

I remember wondering how to set this up when I was taking the PT and I thought that it would be easier to write down the "uncertainty" (how many pieces does each person move?) as opposed to the "certainty" (each piece of furniture is moved by two people). I thought the "certainty" would be easier to juggle in my mind, off paper.

Any advice for determining which variable to use as the base in ASSIGNMENT games? I know that for ordering games, the variable with the most logical "order" should be used, but how about in games like this?

Thanks!

[megm7267]

Quick question on this -how do you write the contrapositive of a biconditional..is it the same as writing it for a conditional?

[megm7267]

The posted walkthrough is incredible! It pretty much answered all my Qs

[noah]

Quick question on this -how do you write the contrapositive of a biconditional..is it the same as writing it for a conditional?

Glad you liked Matt's write-up.

As for this question, yes, it'd be the same.

T < -- > ~ M can be considered T --> ~ M and ~ M --> T, so then take the contrapositive of each of those.

Or, get fancy, and negate each side of the double-arrowed statement, and you get ~ T < --> M.

[steves]

I appreciate Matt's full solution posted above. In the course of the full solution, Matt plugs options from the questions into new diagrams many times. During an actual test or PT, should we be drawing out new diagrams that many times? I know we've been taught not to plug question-specific conditions or options into the main diagram. But it takes a lot of space and time to draw so many diagrams during an actual test. This particular diagram isn't so huge, but I've run into similar uncertainty on how often to re-draw more complicated diagrams or frames--with all their inferences that are easy to make mistakes copying.

[ManhattanPrepLSAT1]

Good question Steve, this is important!

On a game like this, I think a lot of folks would feel very comfortable recreating a new game board next to each question. But there are many games out there (particularly open grouping games where you don't know how many times each player goes) where you make a ton of upfront inferences and recreating the game board is not such a good idea (think PT35, G2 - Cars with Different Options). For games like those, it may make more sense to circle permanent features on your game board and plug things in around them, removing them as you move on to the next question.

In the end, there's a lot of preference involved in the decision to recreate game boards or remove previous work from a hypothetical before moving on. Find what works best for you―which may vary according to game type!

[dontmesswmeow]

I would like to redress the error in the 'Matt's explanation on question11 within the Setup thing of Game #2.

For the last question (11), the last slot that should go along with G for recliner moving should be M, NOT 'either J or M', unlike the attached explanation suggested.

This is because of the last rule, which says G can't go with J.

Hope this helps!

[JohnnyL721]

For the rule "If Josh helps move the table, then Maria helps move the recliner", are we not supposed to write out the contrapositive for this as well? (If M does not help move the recliner, J does not help move the table).

[ohthatpatrick]

"supposed to" is kind of subjective.

Sometimes we leave the contrapositive off our diagrams just to keep them cleaner looking. Similarly, that's why a student might choose to not write the contrapositive on her page: if the game setup is looking pretty complex and overwhelming, then sometimes it's nice to have less to look at.

We never NEED a contrapositive, as long as we're comfortable thinking through the contrapositive when we look at a conditional rule. But most of us (teachers included) do have the policy to pretty much always write the contrapositive, since it gives your brain an easier way to see when that's being triggered.