Law School Discussion

Test 36 - Dec'01, sect 4, Q. 1-6 (Fruit stand)

nemo

Test 36 - Dec'01, sect 4, Q. 1-6 (Fruit stand)
« on: September 10, 2005, 05:40:38 PM »
These kinds of games are killing me...  :-\
Could anyone advise on the correct way to approach them? THANKS  :)

A fruit stand caries at least one kind of the following kinds of fruit: figs, kiwis, oranges, pears, tangerines, and watermelons. The stand does not carry any other kind of fruit. The selection of fruits the stand carries is consistend with the following conditions:

If the stand carries kiwis, then it does not carry pears.
If the stand does not carry tangerines, then it carries kiwis.
If the stand carries oranges, then it carries both pears and watermelons.
If the stand carries watermelons, then it carries figs or tangerines or both.

1. Which one of the following could be a complete and accurate list of the kinds of fruit the stand carries?
a) oranges, pears
b) pears, tangerines
c) oranges, pears, watermelons
d) oranges, tangerines, watermelons
e) kiwis, oranges, pears, watermelons


2. Which one of the following could be the only kind of fruit the stand carries?
a) figs
b) oranges
c) pears
d) tangerines
e) watermelons


3. Which one of the following CANNOT be a complete and accurate list of teh kinds of fruit the stand carries?
a) kiwis, tangerines
b) tangerines, watermelons
c) figs, kiwis, watermelons
d) organges, pears, tangerines, watermelons
d) figs, kiwis, oranges, pears, watermelons


4. If the stand carries no watermelons, then which ofe of the following must be true?
a) the stand carries kiwis
b) the stand carries at least two kinds of fruit
c) the stand carries at most three kinds of fruits
d) the stand carries neither oranges nor pears
e) the stand carries neither oranges nor kiwis


5. If the stand carries watermelons, then which one of the following must be false?
a) the stand does not carry figs
b) the stand does not carry tangerines
c) the stand does not carry pears
d) the stand carries pears but not oranges
e) the stand carries pears but not tangerines


6. If the condition that if the fruit stand does not carry tangerines then it does carry kiwis is suspended, and all other conditions remain in effect, then which one of the following CANNOT be a complete and accurate list of the kinds of fruit the stand carries?
a) pears
b) figs, pears
c) oranges, pears, watermelons
d) figs, pears, watermelons
e) figs, oranges, pears, watermelon

sherm

Re: Test 36 - Dec'01, sect 4, Q. 1-6 (Fruit stand)
« Reply #1 on: September 10, 2005, 06:09:41 PM »
It's an unrestricted In/Out game. You need to create an In/Out diagram, and then accurately symbolize the conditional clues and their contrapositives. What's your specific problem?

Re: Test 36 - Dec'01, sect 4, Q. 1-6 (Fruit stand)
« Reply #2 on: September 10, 2005, 06:19:15 PM »
there is no real catch to that game, is that you haven't done an in/out game?

Re: Test 36 - Dec'01, sect 4, Q. 1-6 (Fruit stand)
« Reply #3 on: September 10, 2005, 06:24:58 PM »
with these type of games i usually just diagram all the conditional statements, and their contrapositives, then try to link statements together. 

r.

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Re: Test 36 - Dec'01, sect 4, Q. 1-6 (Fruit stand)
« Reply #4 on: September 10, 2005, 06:27:45 PM »
Okay, so you have a group of things (in this case six kinds of fruit) and from this group of things will be selected a smaller or equal sized group (to go on th fruit stand). It doesn't matter what order they are selected in, only that they are selected or not selected according to the various conditions. So, we'll end with two groups (the kinds of fruit on the fruit stand, and the kind not on the fruit stand). So the we just go through the rules and make the inferences and this will govern what is selected.

the first rule states that if there are kiwis there are no pears. So K--> no P, and taking the contrapositive of this conditional: P---> no K.

the second rule stas that if there are no tangerines, then it carries kiwis so: no T--->K and  no K-->T. This is a pretty powerful rule as T or K have to be on the cart.

then the third rule is that O-->PW so if both P and W are not on the fuitstand then O is not.

The final rule is W-->F or T (or both). So if there is no F or T, then there is no W. Also, addinig to the previous rule: if O--> PW and ForT or FT. So we know a great deal if O is selected. Also since P must me selected if O is selected and we know that PK can't go together, so we know T must be selected. so now we know that O-->PWT and
the only question is F on the stand or not.

1.  So we can go on to the first questions and for this complete and accuarate list just go through the lists with the rules, one by one, starting with the most powerful and we can start eliminating answers. the rule that there has to be either K or T on the stand is a strong one, and using that we can eliminate A and C. then since we know if O is selected then PWT is also selected, we can eliminate D and E. We are left with B as our answer.

2.  For the second question we have to see which amonst these five fruits could be the only one carried. Well we know the stand has to carry either K or T, and since K is not an option here, the answer must be D) T.

3.  For the third question again we go though the answers with the list of rules, but this time the correct answer is the list that cannot be all on the fruit stand together. well let's try the largest rule here which is O-->PWT and F or noF, but def. not K. we can look at D and E which has O selected, and D could be a list, and since E has K selected, it is clear this is our answer.

4. If there are no watermelons then we know that it does not carry O. And we know it carries P or K of course. So that is OW and P/K that are definitely not on the  stand. Which leaves P/K F and T as possible selections. So that is three kinds of fruit max on the stand and the answer is C. The only way to really come to this answer is go through the answers one by one and testing to see if the answer must be true. Must it be true K is carried? No, because T could be carried too. Does it have to carry at least 2 kinds? It could just carry T, just liek question 2, couldn't it? (our earlier work helped us there) so that eliminates that, and then you will work on C and see that is the answer, so go to the next problem.

5. Well we have to go through each answer to see which one must be false, so with each possibility we try to make a situation where the answer could be true to eliminate it. We know W are there and W--> F or T so A is out. W--> F or T so B is out. There is no reason P couldn't go with W, as a group could be OPWT. PW could exist without O, but if O was there, PW would have to be there so it's a bit tricky, but we can also eliminate D. E is our answer, be confident with your work and move on (but it is right because if P is on the stand and there are no T, then there owuld have to be K but we know K and P can't be on together, ta da!)

6. So this eliminates the T/K rule. Just go through like before and start eliminating. A and B could both be true, but C cant be the list because O-->PW and W-->F or T or both. OS this list is missing an F or T and it is our answer.

Hope this helps, I know what I just wrote must be a mess.

5.



Re: Test 36 - Dec'01, sect 4, Q. 1-6 (Fruit stand)
« Reply #5 on: September 10, 2005, 06:31:42 PM »
once you diagram your rules like you would any other game you make a chart like this:

IN | Out
     |
     |

1. Which one of the following could be a complete and accurate list of the kinds of fruit the stand carries?
a) oranges, pears
b) pears, tangerines
c) oranges, pears, watermelons
d) oranges, tangerines, watermelons
e) kiwis, oranges, pears, watermelons

this is a list question, go through your rules and eliminate them one by one...

a.) If you have O then you have p AND w .... A is wrong
b.) works but keep going
c.) If you have you have P and W but remember if you have W you also have F or T or BOTH... C is wrong
d.) If you have O you have P and W... D is wrong
e.) If you have K you do NOT have P... E is wrong


2. Which one of the following could be the only kind of fruit the stand carries?
a) figs
b) oranges
c) pears
d) tangerines
e) watermelons

*** remember the rule if you dont have T then you have K***
a,b,c,e: all would have to have T
D.) T could be alone

The rest of the games are done the same way just use the in|out chart, dont erase it after you draw one because it can help you with a later answer

nemo

Re: Test 36 - Dec'01, sect 4, Q. 1-6 (Fruit stand)
« Reply #6 on: September 10, 2005, 11:34:00 PM »
These in/out games are kinda confusing, but I think my problem is that I never list the contrapositives...

Big mistake, huh?!   :-\

Thanks for all your contributions. It's now much clearer.  ;D