## Monday, 11 August 2014

### More Venn diagrams with a logic puzzle

A long time ago I posted about Venn and Euler diagrams and I have been meaning to get back to this subject. Coincidentally, it was John Venn's 180th birthday on the 4th of August, celebrated by Google, so I cannot think of a better time to revive the subject.

Firstly, we recall the all important definition: a Venn diagram contains every single possible intersection between all combinations of the sets. This can be compared with an Euler diagram, which only shows the intersections in which you are interested. An illustration of this can be found in Figure 1.
 Figure 1. Using four shapes a basic Euler diagram is not the same as a Venn diagram. The right shows an Euler diagram whereas the left is a Venn diagram, as it contains all possible combinations of the four groups.
As I mentioned, these are great ways of seeing logical information quickly and clearly. To show how useful they are let us consider the following puzzle.
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I have a collection of 8 caterpillars that have a range of different features. They can all be seen in Figure 2, below.
Unfortunately, some of them are dangerous to touch. Equally troubling is that I do not know which the dangerous ones are! All I know is that the following three statements are true:
1. If a caterpillar has blue eyes or spots it is dangerous. If a caterpillar has both, we can't tell if it is dangerous.
2. All safe caterpillars have more than one of the following features: teeth, blue eyes, spots, or spikes.
3. Caterpillars with both teeth and spots are dangerous.
Using just these facts, which caterpillars are safe to touch?

Now of course there are many ways to solve this little puzzle, but Venn diagrams offer a really nifty way of seeing the solution simply and completely. Have a go at solving it and I'll post the solution next time.

1. Venn diagram puzzles are awesome. We have created some quiz type Venn diagrams might want to check them out

2. Many thanks for the reply and the link. I've just had a quick play with your online Venn maker. It is pretty cool and perfectly usable for solving this problem. However, I couldn't find the quizzes you were referring to. Could you provide a link to those?

3. Tip for the caterpillars: 1 should read 'blue eyes or spots'

1. You're quite right. I've edited the text to correct this.

4. Very graphical venn diagram. Don't really understand the Caterpillar diagram though. Its very creative and graphical. You must have used a venn diagram maker for that.

1. What don't you understand about the caterpillar diagram? The diagrams were created in a mixture of inkscape and microsoft word.

5. Why on earth do the caterpillars have spikes all over there bodies? It makes no sense whatsoever. Please help me.

1. i know right

2. They are all dangerous. They should be taken to Area 51 for extraterrestrial analysing. This is ridiculous.

3. Hello L0RD Sonic. How can I help you? The images above are simply a fun way of seeing how to use Venn diagrams. They're not meant to represent actual caterpillars.

4. Thanks for that. The help is greatly appreciated. This was actually a really good puzzle. Thanks.

6. "If a caterpillar has blue eyes or spots it is dangerous. If a caterpillar has both, we can't tell if it is dangerous." well clearly if it had either spots and blue eyes it would be dangerous.

1. Not necessarily. There is such a thing as "exclusive or", which means if we have one or the other condition (but not both conditions) then the property holds. A simple example would be "Everybody in town either shaves himself or is shaved by the barber, who shaves the barber?". Although ambiguous (which is why we have mathematics :) ) it is supposed that we should assume that you can't do both, even though we've used "or".

2. makes no sence

3. What makes no sense? I'll happily try to explain.

4. The fact that youve said that both aare poiseness but if there both together you dont know if there poiseness or not.

5. It could be that the gene for blue eyes provides an antidote for the danger provided by the spot gene and vice versa. For an example that illustrates the opposite idea, there are poisons called binary poisons. The poison is made up of two separate chemicals. On there own, each separate chemical is much less dangerous than the mixture. Thus, I might say that, we know chemical A and B are safe, but together, they might be poisonous.