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I was just playing around with GeoGebra, then I tried to represent four sets $A, B, C, D$ using triangles. It seems correct to me, but I want your confirmation.

If not correct, I hope you bother to state the reason.

enter image description here

dude076
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    I don't think so. There should be $16$ regions, and I only count $13$. I may have miscounted, but I don't think I've missed $3$. – saulspatz Apr 20 '20 at 15:26
  • It is not clear to me what the regions are. It looks like $EDB$, $ACB$, $GIH$ are some of them... but what else? $DCJ$? I only see $12$ regions, $13$ if you count outside of the entire image... With four sets there should be $2^4=16$ regions. – JMoravitz Apr 20 '20 at 15:27
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    Related: Why can a venn diagram for 4+ sets not be constructed using circles – JMoravitz Apr 20 '20 at 15:31
  • I've added a new photo, stretched out stuff and added more points. I believe there are 16 regions If my method of counting is correct. Can you check again? – dude076 Apr 20 '20 at 15:33
  • Did you mean Venn diagram? – J. W. Tanner Apr 20 '20 at 15:37
  • I did. Do you have an answer to my question? – dude076 Apr 20 '20 at 15:37
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    I still count $13$ regions including the outside region. You have not yet clarified which portions of the figure correspond to which set... but if I was right that $DCJ$ is meant to be the "blue" set... then where does the "blue" set overlap with the orange? – JMoravitz Apr 20 '20 at 15:38
  • It doesn't. I think that proves my construction is not correct. Thanks for your help. – dude076 Apr 20 '20 at 15:40
  • But I have a question, If we picked J on GH, would that make the construction correct? – dude076 Apr 20 '20 at 15:41
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    Then where would blue overlap with black and orange without overlapping with red at the same time? Place $J$ even a bit further below $GH$. I think that might fix it... it is hard to tell without seeing it. Still, this construction is hardly convenient. The constructions alluded to in the linked question are much easier. – JMoravitz Apr 20 '20 at 16:03

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As pointed out in the Comments, you're missing various regions. Here's one with 4 triangles that does work. I tried to use 1 right angled (blue), 1 isosceles (red), 1 equilateral (green), and 1 scalene (black) triangle, so you can use this Venn diagram to classify various triangles. :)

enter image description here

Bram28
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  • Thanks! But I have a question. How do we count regions? I just count everything in which borders are lines we drew. Is this method correct? or do we just brainstorm every set that can be constructed from 4 sets? Is there a systematic way to do this? – dude076 Apr 21 '20 at 10:56
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    @HassanAshraf This diagram has 16 regions, corresponding to the 16 possibilities of either being inside or outside each of the triangles. Note that one of those possibilities is to be outside of all the four triangles. so that's the 'outside' region ... which isn;t really 'bordered by anything. It took a bit of trial and effort to draw the triangles so that you indeed get these 16 regions, thoguh there is a basic method for this: (continued) – Bram28 Apr 21 '20 at 12:14
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    @HassanAshraf The basic method is this: start with one enclosed figure. Then draw a second one that goes inside the first and out. Then a third that follows that same trajectory that the second did, but that crosses the second one exactly once before the second one makes any crossing. The fourth now follows that trajectory, but corsses the third one exactly once between any crossings that the third one makes. Etc. (continued) – Bram28 Apr 21 '20 at 12:17
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    @HassanAshraf If you can make the enclosed figures flexible, you can always do this, meaning that a Venn diagram is possible for any $n$. But with constraints on the figures, a Venn ddigram made of those figures may become impossible. Apparently you can make a Venn diagram out of 6 triangles, but probably making one for 7 triangles is impossible, juts like a Venn diagram made of 4 perfect circles is impossible. – Bram28 Apr 21 '20 at 12:19
  • So we count any geometric figure in the diagram, plus the outside region. Doesn't matter whether it is convex or concave, regular or not. Am I right? For example, do we count DMG, DGPJM as regions or not? – dude076 Apr 21 '20 at 17:43
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    @HassanAshraf DMG Yes. DGPJM No. DGPJM consists of 2 regions: DMG and GPJM – Bram28 Apr 21 '20 at 17:52