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# Venn-diagram

Posted on 2010-11-18
Medium Priority
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How would a Venn diagram be for this?

(A - B)c n(B - C)c n(C - A)c

I dont want you to solve it but to explain how to solve it step by step. So i dont just need an answer
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Question by:Mickeys
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LVL 27

Expert Comment

ID: 34163757
What do the "n" and "c" mean?

Draw three circles so you have all the possible overlaps:

A  B  C  AB  AC  BC and ABC

and start carving it up.
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LVL 27

Expert Comment

ID: 34163780
There is a 3-circle Venn Diagram Template here:

http://www.conceptdraw.com/en/products/cd5/ap_venn_diagram.php
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Author Comment

ID: 34164046
(A - B)c u (B - C)c  u(C - A)c

the u should be turned upside down.
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Author Comment

ID: 34164115
Like this. But what more?
Namnl-s.jpg
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LVL 37

Expert Comment

ID: 34165469
Shade (A-B)c, (B-C)c and (C-A)c and see what the intersection is. Then shade just the intersection for the answer.

What does the little c mean? Is it the not operator?
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Author Comment

ID: 34165508
so I did your first step. But I dont understand the next one. that is where I get stuck. :-)
Namnl-s2.jpg
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LVL 27

Expert Comment

ID: 34165537
I don't think that is correct.

(A-B) should include some of C.

And what does the the little "c" mean?
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Author Comment

ID: 34165560
so like this?
Namnl-s3.jpg
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LVL 37

Expert Comment

ID: 34165628
Make one venn-diagram for each one and see which regions are shaded in all of them.

What does the little c mean?
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Author Comment

ID: 34165685
???? You mean split them up?

I have no idea what the little c is
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LVL 37

Expert Comment

ID: 34165715
Well you need to find the intersection, so you need to find each of the three separately and see which areas all are in.
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Author Comment

ID: 34165723
well I dont need to split them up for that. I can see it is the big part in all of them. right?
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LVL 37

Expert Comment

ID: 34165724
The little c means compliment which is the same as 'not'
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LVL 37

Expert Comment

ID: 34165736
Not just the big part. But you're close.
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Author Comment

ID: 34165756
I am so stupied with math. :-(

well i can see the big part......and then the outside of course
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LVL 37

Expert Comment

ID: 34165812
Look at the venn-diagram for (A-B)c. What areas will be in all three pieces?
venn.png
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Author Comment

ID: 34165848
well the half moon. But if I see at my diagram I can get the orange and green a half moon but the last color I cant get that to a half moon. Hmmmmm
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LVL 37

Expert Comment

ID: 34165918
The half moons are unshaded in (A-B)c
Your green half moon is wrong. Yours is (B-A) it should be (B-C) but you need (A-B)c and (B-C)c. c is complement so you should shade everything EXCEPT the half moon.
Just look at the figure on the right side in mine. Red is the (A-B)c the white is the stuff that's already out.
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Author Comment

ID: 34166032
sorry to stupied to figure this one out?

So the one picuter I added last is wrong? Is that what you mean?
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LVL 37

Expert Comment

ID: 34166133
Yes. It has a few problems. Look at the figures I posted. The left one shows (A-B) which is just a step to getting the one on the right side which is (A-B)c represented by the red color.
So what would (B-C)c and (C-A)c look like? Then which areas are common to all three?
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Author Comment

ID: 34166233
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LVL 37

Expert Comment

ID: 34166275
Yes except the half moons will be somewhere else of course.
Do it in three steps.
For (B-C)c
Find B, then remove what is also in C then invert the whole thing. You should get the half moon in the right spot.
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Author Comment

ID: 34166307
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LVL 37

Expert Comment

ID: 34166456
Okay. Is the white supposed to be the answer or the yellow? It's not right at all.
Show me all three
(A-B)c
(B-C)c
(C-A)c

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LVL 27

Expert Comment

ID: 34166479
Note that this is a very symmetric problem.

Go back and look at TommySzalap's picture for (A-B)c.
It includes everything but the crescent moon shaped section that is (A-B).

What does (B-C)c look like?
What does (C-A)c look like?

What does the intersection of all three look like?

It is going to be symmetric.
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Author Comment

ID: 34166537
new try
Namnl-s5.png
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LVL 27

Expert Comment

ID: 34166608
(A-B)c is correct.  The others are missing the little triangular shaped piece in the center.
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LVL 37

Expert Comment

ID: 34166625
Yeah, the middle should be yellow in all of them.
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LVL 37

Expert Comment

ID: 34166634
Since the middle is in C it WON'T be in (B-C) so it WILL be in (B-C)c
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Author Comment

ID: 34166635
ok. so where they all meet should be filled. But what is the answer then? Is the answer all three pictures??????
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LVL 37

Expert Comment

ID: 34166713
What sections are yellow in all three pictures?
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Author Comment

ID: 34166730
well if I add that yellow to the things I missed. It will be that part plus the section below that. so two sections are yellowed on all parts
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LVL 37

Expert Comment

ID: 34166806
Oh. Sorry. Your (B-C)c is still wrong. You did (B-A)c again.
So the parts yellow in all are the little center triangle and the outer area (as you mentioned before)

This makes sense if you work it out logically too. (If this confuses you ignore it)
A-B = A n Bc     Subtraction rule
(A-B)c = (A n Bc)c = Ac u B     De'Morgan's Law

So the whole thing is (Ac u B) n (Bc u C) n (Cc u A)
=>  (Ac n Bc n Cc) u (A n B n C)
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Author Comment

ID: 34166835
So here is the answer. You should really be gratful that I can help you people solve this problem
;-)
Namnl-s5.png
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LVL 37

Expert Comment

ID: 34166849
Ach, and you did (C-B)c instead of (C-A)c
For (B-C) shade B then unshade C. Then invert the whole thing to get (B-C)c
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LVL 27

Expert Comment

ID: 34166854
Not quite done....
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LVL 27

Assisted Solution

d-glitch earned 400 total points
ID: 34166884
What about the corners of the square...
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Author Comment

ID: 34166898
I give up. I dont understand shit. What should really the solution look like?
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LVL 37

Expert Comment

ID: 34166903
You missed the outer part.
Study this and figure out why it is the correct solution.
Namnl-s5-corrected.png
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LVL 27

Expert Comment

ID: 34166944
Bingo.  You have mastered a skill which has no future economic benefit.
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Author Comment

ID: 34166971
Namnl-s5.png
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Author Comment

ID: 34166978
ah....I almost got it. i just saw your correct version.
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LVL 37

Accepted Solution

TommySzalapski earned 1600 total points
ID: 34167042
Yes. Yours was right except you just didn't see the outside part.
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LVL 37

Expert Comment

ID: 34167044
Excellent.
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Author Closing Comment

ID: 34167069
haha. It was really  hard to solve. I dont understand how you can have it so easy to understand this. I got one more in here....but I think I will save my brain for that until tomorrow. Need to study this one first. Thx guys
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