Lesson 3 homework

[jessicamorehead]

Game 3: June 1995 pg 3-50

Hi, I am confused about the inferences that were made here. I understand that T and J cannot be next to each other, regardless of their order. However, how do you know that the inferences have to start with T? And how do you know which number?

The correct inferences in the back of the book are listed as:
T2 --> J4
T3 --> J5

Couldn't the inferences be different? Such as:
J2 --> T4
J3 --> T5

Also, couldn't T be on 1 or 6? So inferences from that would be
T1 --> J cannot be on 2
T6 --> J cannot be on 5


Any help is appreciated! Thanks!

[Adam Tyson]

Thanks for the question, Jessica! The choice as to which terms to make sufficient and which ones to make necessary in your inferences will come down to the logical relationships between the variables. Which one is the "powerful" variable in the relationship, forcing the other one to do something? That's the sufficient condition. The one getting forced around? That's the necessary condition. You can often make conditional claims where one element, like T in the 3rd position (T3)) is sufficient for one thing but necessary in the presence of another. That might lead you to make a conditional chain, which can be very powerful!

The inferences in the back of your book should read:

T3 J5 (because J could not be in 1, 2, 3, 4, or 6 at that point due to the two rules about not being 1st or 6th and not being next to T)

and

T4 J2 (because J could not be in 1, 3, 5, or 6)

My copy of that book has no inference of T2 J4, and that would be a false inference because with T in 2, J could also be in 5. If yours has such an inference, that's a typo - please take another look and let us know!

You're right about T2 J3 and T6 J5, although those seem a bit redundant since we know those two can never be next to each other. The ones we added were more interesting because they were more powerful - they told us not just where J could not go, but exactly where J must go in those two situations.

Your other two inferences, though, appear flawed to me. If J is in 2, T is not forced into slot 4, because T could also be in 5 or 6. When J is in 3, T is not forced into slot 5 because T could then be in slot 1, or 5, or 6 - anywhere not next to J.

Double-check the inferences in the explanation and let us know if there is an error there. Going forward and making your own inferences, focus on the powerful relationships that force something to happen, and less on the ones that force something to not happen. Typically it's the former that will lead to answering questions, while the latter does so less often.

Good luck, and keep at it!