April 8, 2016 at 6:21 pm #1696jpoznan0587Participant
Can you please put the explanations for the extreme links drill in The Trainer??
I understand that it comes from sections in LT 13 and LT 18- but I don’t understand how alot of the links are made and it would be super helpful if you explain the chains past the first drill. Would be SUPER helpful, thanks !
April 12, 2016 at 8:35 am #1701
Sure thing —
Two notes — I’ll be using > in place of arrows, because I can’t type arrows — & I’m going to write each solution in two parts — first the translations of the original conditionals, then the solutions to the given q’s — figured it would be better for your practice / review —
I’ll be posting them as I get them typed up — hope they help, and let me know if you have any follow-up —
BTW, if anyone wants a copy of the exercise we are discussing, here’s a link —
The exercises are on pages 460-461, and they are not for the faint at heart —
April 12, 2016 at 9:26 am #1705
Cheaters Q Solutions
A big key here is to recognize that we know of one combination (W &
B) that leads to public adoration, but we don’t know anything about any other ways of getting public adoration.
1. Y. All winners win and never brag, so all winners have characteristics sufficient to get adoration from the public.
2. N. We don’t know what else might lead to adoration and we aren’t told any reason why cheaters can’t get adoration.
3. N. Again, we know of one way to get adoration, but that need not be the only way — maybe a braggart can be adored by the public for other reasons.
4. N. For same reasons as above 2 problems – we don’t know of other ways to get public adoration.
5. Y. We know cheaters dream of winning, and they never get to win, so we can infer that they don’t get to do everything they dream of doing.
6. Y. All winners dream of winning, and all winners win, and so they all get to do something they dreamed about.
7. N. Not bragging doesn’t guarantee victory.
8. N. We only know of two things they dream of — winning and bragging about it — and we know they don’t get to do these things.
9. N. We know of some people — winners — who dream about bragging but are also adored.
10. Y. All winners dream of bragging, and yet they all don’t do it — thus all winners don’t get to do something (bragging) they dream about doing.
April 12, 2016 at 11:10 am #1707
Students Q Solutions
- N. We don’t know anything about people other than students and parents.
- N. See reason for above.
- N. No guarantee that being a student leads to riding on the bus. Certain students not riding on the bus wouldn’t vidolate any rules.
- Y. P >
- N. No guarantee that being a student and wearing a tag leads to riding on the bus.
- Y. Some parents wear name tags, and these parents are not allowed to ride on the bus. Thus some people who wear nametags are not allowed to ride on the bus.
- N. We know about parents, but there might be other types of adults (such as the bus driver or teachers).
- Y. R > U, R > N: so, R > U & N.
- Y. Contrapositive of above.
- N. Some students could not ride the bus without violating any of the rules.
April 12, 2016 at 3:10 pm #1710
RD > GS ;
GS> RD RD> PS ; PS> RD
Only one dress at a time.
H > PD ;
N > H ;
Note there are some inferences that can be made upfront that can end up helping w/the q’s — in particular there is an important inference that could be made about the relationship between the purple dress and red dress.
April 12, 2016 at 3:27 pm #1711
- N. Can wear glass slippers w/diff colored dress w/o violating any rules.
- N. If it does not wear glass slippers, it won’t wear the red dress. This does not mean the doll has to wear the purple dress. There could be other colors.
- Y. If it wears a purple dress, it can’t wear the red one, and if it doesn’t wear the red dress, it must wear purple slippers.
- Y. If it wears a necklace it must wear a hat, and if it wears a hat that must mean it has on the purple dress, PD >
- N. Again, we don’t know of other dresses, and there is nothing that says the doll has to wear a dress.
- Y. RD >
PD> H> N
- N. A doll wearing a hat and no necklace wouldn’t violate any rules.
PS> RD > PD> HIn words: If the doll doesn’t wear purple slippers, we know it had to wear the red dress, which means it couldn’t have worn the purple dress, which means it couldn’t have worn the hat.
- N. The doll not wearing a necklace doesn’t allow us to infer anything else.
- Y. If it wears a necklace it must wear a hat, and if it wears a hat it must be wearing the purple dress.
April 12, 2016 at 3:47 pm #1713
- N. We have no information about how much lumber is discounted.
- N. The amount of E wood + non E wood outside could be greater than the amount of E wood inside.
- Y. All plywood is exact cut, and no exact cut wood is discounted, so no plywood is discounted.
- N. All plywood is exact cut, and no exact cut wood can be discounted, so no plywood is discounted.
- Y. All the plywood is exact cut, and this puts us at exactly 50% of wood being exact cut. We know that some lumber is exact cut, and so adding whatever that amount is to 50% will create a majority.
- Y. All plywood is exact cut, and no exact cut wood is discounted, so no plywood is discounted.
- N. Of the exact cut wood split up between inside and outside, we don’t know how much of what stayed inside is plywood and how much lumber.
- N. Same reason as above. Could be true that amount of exact cut plywood outside is greater than total amount of exact cut and non-exact cut lumber outside.
- Y. We know majority are cut to exact dimensions, and these cannot be discounted, and so we know the majority cannot be discounted.
- N. We don’t know enough about the amount of non-exact cut wood or discounted wood inside to make this assessment.
April 12, 2016 at 4:09 pm #1715
- Y. We get this from combining first two statements.
- Y. We know there is at least one unhealthy dish on special, and all dishes on special come with the customer’s choice of fries or soda.
- N. We know stuff about specials on the chalkboard, but not about other things that might be on the chalkboard.
- Y. We know that all specials on the board, and some of these specials are unhealthy.
- N. See #3.
- N. Tempting, but we don’t have enough info to infer this. The board could have a majority of healthy dishes and still satisfy the given rules.
- N. We don’t have info that allows us to make this inference about healthy dishes.
- Y. We know most dishes are offered on special, and all that is offered on special goes on the board — this is enough to infer that most dishes go on the board.
- Y. Since we know that the specials constitute the majority of total dishes, and all specials are on the board, there is no way the number of non-specials on the board can be greater.
- N. We don’t know about the exact overlap between dishes that are unhealthy and those on special, and so we can’t guarantee this inference.
November 19, 2016 at 10:23 am #2858jeremybenthamParticipant
thanks for the post Mike; this should probably have been included in the book — also would have been nice to have them numbered.
could you double check lumber #9? I dont think we can confirm this.
would you also be able to create some more exercises similar to this but for sufficient assumptions?
love the book 😉
November 21, 2016 at 9:25 am #2867
Hi Jeremy —
Thanks for your thoughts and I’ll certainly keep your suggestions in mind for future versions of the book —
In terms of #9 —
We know that 1/2 the wood is lumber and 1/2 plywood.
We know all the plywood is cut to exact dimensions.
We know some of the lumber is cut to exact dimensions.
We can add the above three statements together to infer that most of the wood is cut to exact dimensions.
Next, we know that wood cut to exact dimensions cannot currently be discounted.
So, we can conclude that most of the wood is not currently discounted.
Let me know if I’m missing something — otherwise hope that clears it up —
Take care — Mike
January 31, 2017 at 8:16 pm #2972TimParticipant
Hey Mike, I”M still having a lot of trouble with the doll problem. specifically the 1st statement.
If a doll is wearing a red dress, it will be wearing glass slippers. If the doll wears any dress that isn’t red, it will wear purple slippers. Doesn’t that mean the only dress it can wear glass slippers with is the red one, making it provable and thus a Y? I just don’t understand how a situation could exist where the doll wears the glass slippers with any dress that isn’t red, because if the dress isn’t red it must be wearing purple slippers.
Help is appreciated, thank you!
February 1, 2017 at 9:29 am #2973
Before I start, just a random coincidence / side story —
I had an exterminator come to my house yesterday, and he was literally wearing two pairs of shoes at the same time — his regular shoes, then some strange giant slipper sort of protective shoe over it — I wanted to ask him if I could take a picture of it, in my head specifically thinking of this particular drill scenario, but I felt too shy and didn’t ask him — and then your question came in! I feel great regret about this.
As you suggested in your separate email, there is nothing that restricts the number of shoes the doll can wear.
I do give a small hint with the phrase – “the doll can only wear one dress at a time” — which could tip you off that there aren’t restrictions on the # of hats or slippers the doll can wear (would be much easier/more obvious if I reversed the roles that shoes and necklaces play in the q).
I get it that this is a particularly cruel way to design the drill — please don’t hate me for it! — but these specific drills are meant to be extremely difficult, and I really wanted to push the limits in terms of testing your ability to not make unjustified assumptions, no matter how reasonable they may seem —
HTH — Mike
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