[Ap0C552]

I am asked to make a venn diagram of the following sets but don't know what the little C next to some of the letters means.

Does anyone know?

Ac∩Bc∩C = Ac∩B∩Cc

Question 6 on this page to see if in context.

http://www.cs.umanit...0/CS2130A1.html

[AdamSpeight2008]

That's a new one for me also. So I look it on
http://en.wikipedia....ematical_symbol
And it directed me to
http://en.wikipedia....f_the_continuum

[smohd]

Not sure, but I think he mean complement like saying:

 A'∩B'∩C 

[Ap0C552]

Yes I figured out that it means compliment.

Now I have another question.

On the assignment it says show that

Ac∩Bc∩C = Ac∩B∩Cc = ∅, B ≠ C, and B ∩ C ≠ ∅.

But


Ac∩Bc∩C is...





Ac∩B∩Cc is...



Neither of those sets are equal and neither can equal the empty set.....pretty confused here LOL.

[r.stiltskin]

Complement.

"You draw nice pictures" is a compliment.

All kidding aside, you are overlooking the third assumption: B ∩ C ≠ ∅.

[Ap0C552]

OMG I though it was B ∩ C = ∅. LMAO.

Ok so now what does that exactly when B and C ≠ empty set?

Does that simply imply that B overlaps C? Does this mean that A does not overlap anything?

Because if B and C do overlap the diagrams would be different, but this would STILL not be true Ac∩Bc∩C = Ac∩B∩Cc = ∅

[r.stiltskin]

Don't say "B and C ≠ empty set", say B intersection C ≠ empty set.

So yes, if the intersection of B and C is NOT the empty set, then it must be that B and C have at least some elements in common. This could mean that B equals C, or that B includes all of C, or that C includes all of B, or that B and C partially overlap.

You are given that B does NOT equal C, but any of the other 3 cases is possible.

You are not given any information about A. A might include all of B and all of C, none of B and all of C, none of B and part of C, none of B and none of C, and various other possibilities ... Since you are only asked to make a single Venn diagram presumably you can choose any of those to illustrate.

[Ap0C552]

r.stiltskin, on 04 October 2011 - 07:51 PM, said:

Don't say "B and C ≠ empty set", say B intersection C ≠ empty set.

So yes, if the intersection of B and C is NOT the empty set, then it must be that B and C have at least some elements in common. This could mean that B equals C, or that B includes all of C, or that C includes all of B, or that B and C partially overlap.

You are given that B does NOT equal C, but any of the other 3 cases is possible.

You are not given any information about A. A might include all of B and all of C, none of B and all of C, none of B and part of C, none of B and none of C, and various other possibilities ... Since you are only asked to make a single Venn diagram presumably you can choose any of those to illustrate.

Ok now I am stumped as to how to make this happen.

NVM LOL its just B and C overlap all inside A.

This post has been edited by Ap0C552: 04 October 2011 - 08:13 PM

[r.stiltskin]

It's not so difficult. You just have to play around with different sizes and arrangements of the circles. First choose some arrangement of B and C that satisfies the last two constraints, and then figure out where to put A to satisfy the first two.

[Ap0C552]

Thanks for your help!

It is really appreciated!