# A logical question

1. Aug 24, 2008

### transgalactic

data:

every body who has a blue eyes has a short tail .
every white bunny has a blue eyes.

which one of this arguments when added to the data
leads to the conclution
"tom is not a rabbit" .

A.the eyes of tom is blue and his tail is short.
B.tom is white and he has a long tail.
C.tom is black and his tail is short.
D.tom has a green eyes and he has a long tail.

what is the algorith for solving such a question.

2. Aug 25, 2008

### regor60

Just use Venn diagrams and it will demonstrate B

3. Aug 25, 2008

### transgalactic

i drawed many circles representing each group
and subgroup

i dont how to solve this kind of question
usin Venn

4. Aug 25, 2008

### davee123

Venn diagrams probably won't help much here, because you've got 4 overlapping categories-- tail length, eye color, species, and color. With 3 overlapping characteristics or fewer, Venn diagrams are great. But when you get to 4, suddenly you can't stick with the traditional Venn "circles", and have to switch to bizarre other shapes. And with 5 categories, I don't even think it's possible to show all the conceivable overlaps.

For this problem, attack it just like every other logic problem. Try each suggestion, and see where it takes you:

A.the eyes of tom is blue and his tail is short.

Can Tom be a rabbit? Let's assume he is a rabbit, and see if we get any contradictions:
We know that if he has blue eyes, then he has to have a short tail. Well, that's ok. We also know that every bunny that's white has blue eyes. And we don't even know what color Tom is in this situation. So no contradictions.

B.tom is white and he has a long tail.

Again, assume Tom is a rabbit. We know that if he has blue eyes (which we don't know in this case), he has to have a short tail. So, no problems yet. But next we know that every white bunny has blue eyes. And as it turns out, we know that Tom is a white bunny. Therefore, we know he *HAS* to have blue eyes! Acha! Well, with this new piece of information, we have to go back to the first rule and see if we have any brand new contradictions. Turns out we do. We now know Tom's eyes are blue, which means that he HAS to have a short tail. Unfortunately, Tom has a LONG tail. So this contradiction means that our assumption (that Tom was a rabbit) must be FALSE. Tom cannot be a rabbit.

C.tom is black and his tail is short.

Again, assume Tom is a rabbit. If he has blue eyes (nope!) then he has to have a short tail. No contradictions. And if he's a white bunny (nope! He's a black bunny), then he has to have blue eyes. Again, no contradictions.

D.tom has a green eyes and he has a long tail.

Ok, one last time, assuming Tom's a bunny. If he has blue eyes (again, no!) then he has to have a short tail. No problem. And we know if he's a white bunny (we don't know his color), then he has to have blue eyes. So he could be an orange bunny, and we'd have no problems.

DaveE

5. Aug 25, 2008

### regor60

Now, do you think I said Venn diagrams because it didn't work ? Just to provide some misdirection, perhaps ?

It worked fine for this example, for me at least ;)

6. Aug 25, 2008

### davee123

I didn't say they couldn't work-- I actually tried using a Venn diagram for a couple minutes and became utterly confused trying to apply things in order, since white bunnies (but not other color bunnies) were totally encompassed within blue-eyed creatures, which were totally encompassed within long-tailed creatures, which said nothing of how to draw pleasantly round circles to illustrate the point. I could do it with various unrelated bubbles (IE having a bubble for white bunnies and other bubbles for other colored bunnies), but that sort of defeated the purpose of making a useful visual aid, since the bubbles weren't necessarily adjacent. Also, I could represent things with non-circular shapes, but again, it started looking confusing pretty fast.

Again, it's not that you can't get it to work-- it's that I found it to be grossly unhelpful in this instance. By contrast, I probably spent about 2 minutes trying to draw Venn diagrams before saying "screw this", at which point I solved the problem in about 30 seconds or so just by following the logic as stated.

I would, however, be curious to see how you arranged your diagram, assuming you used 4 circles to represent the 4 traits. All of my diagrams looked kind of patched together since I had little related-but-not-touching bubbles and/or non-circular shapes that I didn't like.

DaveE

7. Aug 26, 2008

### davee123

Well, I feel silly. For whatever reason, I woke up this morning and figured out why my Venn diagrams were totally wrong. I had been drawing "white bunnies" as a distinct circle, rather than an intersection.

DaveE

8. Aug 26, 2008

### regor60

yes, that's how white bunnies were represented in mine as well (intersection). But you're right, probably could have solved it sooner w/o Venn

9. Aug 26, 2008

### transgalactic

so ill learn how to implement it on other questions
i need to solve this kind of questions in one minute
unlike the previos stuff

how do i solve it in a minute

Last edited: Aug 26, 2008
10. Aug 26, 2008

### regor60

1. draw a big circle. label it "everybody"

2. within the "everybody" circle, draw another circle. label it "short tail". therefore, everything outside this circle has a long tail.

3. within "short tail" circle draw a circle. Label it "blue eyes"

4. draw the last circle within "everybody" and partially intersecting the "blue eyes" circle, but not entirely within "short tail" Label this circle "bunnies". Further, label the intersection of "bunnies" and "blue eyes" as "white bunnies"

By reading the choices and inspecting the diagram, you can see that since all white bunnies are contained within the blue eye circle, and the blue eye circle is completely contained within the short tail circle, that the only way Tom could be a rabbit and be white, is if he has a short tail, therefore, if he has a long tail per B, he can't be a rabbit and so the answer is B

whew ! good luck on the minute time limit

11. Aug 27, 2008

### transgalactic

thanks

12. Aug 27, 2008

### davee123

Ahh, but then you don't have a section for white things with long tails, which was part of why things started looking... strange. See attachment.

As stated, though, with Venn diagrams, don't bother drawing it out if you've got a 1 minute time limit. Maybe if the same diagram is applicable for a bunch of related problems, but otherwise, it might be more time consuming than just going through things on your own...

DaveE

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