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I just did this game from the logic games bible and tried making a chain as I think this will help me with in/out games, however can someone look over what I did because the bible says T can be in with Y, but my chain shows the following ( so i thought T and Y cant be together):

U-->S-->W-->/T-->-->R-->Y

Contra:

/Y-->R-->T-->/W-->/S-->U

Also, when making a chain, how do you approach putting it together? Meaning do you look at the rules in order or look at the rules that have variables in common and then start making the chain and can the chain be compiled of the original rules and contrapositives or you can only make a chain using the original rules/contrapositives?

Here are the rules and their respective contrapositives:
1) S → W; ~W → ~S
2) U → S; ~S → ~U
3) ~Y → R; ~R → Y
4) W → ~T and ~R; T or R → ~W

Note that you can break the fourth rule into two pieces if you like.
4.1) W → ~T; T → ~W
4.2) W → ~R; R → ~W

Generally, hopping from rule to rule looking for common terms is the easiest way to chain them. Starting with the elements in the first rule, you can link the terms from the second and fourth rules. Once you've incorporated the fourth rule into the chain, you can then link ~R through the contrapositive of the third rule. From there, you can reverse the arrows and negate (positives to negatives and negatives to positives) all the terms to form your contrapositive chain. Your two chains should look like the following:


In order to establish that T and Y cannot be in together, there would have to be a path which created a T → ~Y or a Y → ~T relationship. Since there isn't such a path in this game, they can be in together.