Can Venn diagrams have more than 2 circles?

Question

I'm trying to to a Venn diagram for A intersect (A union B) = A, where U=anything. But cant seem to do it in 2 circles

Dont quite get how you would fit it into 2 circles, I got 3 with set A, B and (AuB) and An(AuB) is in the intersect between A and AuB. Doesnt that show An(AuB)=A?

Answer 1

Yes, it can have as many circles as needed.

To do A intersect (A union B), first color in both A and B and the part that joins them.

Then color in A again, including the middle part.

Answer 2

Yes, Venn diagram can have more than 2 circles. Each circle represents a set. In your question, there are only 2 sets (A&B) so you only need 2 circles.

A union B is represented by both circles and then intersect with A which is circle A. QED.

Answer 3

Yes, Venn diagrams can have more than two circles, e.g. A, B and C.

In An(AuB), AuB would be the two circles including their intersection area. If A is intersecting the two circles, then
An(AuB) is the same as A itself.

Answer 4

Technically speaking, yes, a Venn diagram may have as many circles as there are equations in the mix. If it helps, you can think of this in non-math terms where you have 3 sets of people. C++ literate, VB literate, and Java literate. There will be overlap between C and VB, as well as VB and Java and Java and C. There will also be a group that knows all three. This link doesnt show this, but shows multiple areas intersecting.

http://tieguy.org/events/2004/gnomesummit/marketing-notes/venn-diagram.png

As for your specific question above, Im not sure I quite follow the equation in effect. It almost sounds like A is just a circle within B or vice-versa.

Answer 5

Yes - they can have more than two circles. (The Stained Glass window at Caius College, Cambridge, commemorating John Venn - after whom the Venn diagram is named - has three over lapping circles http://en.wikipedia.org/wiki/Image:Venn-stainedglass-gonville-caius.jpg )

I think your problem only requires two circles though.

There are three cases to consider:
[1] - B is a subset of A;
[2] - B has a null intersection with A;
[3] - B has a non-null intersection with A.

Case 1 - you have one circle (B) completely within the second (A). The third 'virtual' circle is simply the A circle again.

Case 2 - you have two non-overlapping circles B and A.

Case 3 - you have two overlapping circles.

Answer 6

Yes, venn diagrams can have as many circles as you want. In fact, they don't even have to be circles. It's just a way of representing certain kinds of sets.

However, I don't think your question does require more than two circles anyway.

Answer 7

Venn diagrams can have as many circles as needed. In your case, A is completely encircled by B.

Answer 8

It is more interesting when there's more than one circle!
Suppose A is contained in B.

Answer 9

sure can. we were doing them in maths the other day becasue we were doing probablility and we had one with 4 circles. but yeah they can have as many as you want.

Answer 10

Yes, you didn't answer the actual question, which was "Find n(B)".