Venn Diagram question
I completely DO NOT understand the Venn Diagram and how to use it.
Use a Venn Diagram and the given information to determine the number of elements in the indicated set.
n(U) = 94, n(A) = 41, n(B) = 36, n(C) = 29, n (A∩b) = 6, n(A∩C) = 3, n(B∩C) = 4 and n(A∩(B∩C)) = 1
Find n(A∩(B U C)').
I have tried to draw out the circles and all that does is confuse me even more. This is my last question to figure out and I am completely STUMPED!
I have attached a .jpg showing the diagram you need with the eight regions denoted by the numerals i through viii.
Originally Posted by wilsoac
Region vi represents A∩(B∩C). Start there, by writing the number 1, since n(A∩(B∩C))=1. Then work outwards:
- Regions iii and vi taken together represent A∩B, which contains 6 elements altogether, 1 of which we have just entered in region vi. So region iii must contain 5. OK? So write it down in region iii.
- Then move on to region v. Together with vi, this represents A∩C. We already have 1 element in vi. So how many are left for v?
- Then fill in vii in the same way.
- Then look at the whole of set A. It's made up of four regions: ii, iii, v and vi. It contains 41 elements altogether and you've already tracked down where most of them go. The rest are in region ii. So work out how many are left and write down the answer in region ii.
- Do regions iv and viii in the same way.
- Finally, you can work out how many elements are left to go in region i, by subtracting the number you've already entered from 94.
Then, to answer the question: (A∩(B U C)') represents the elements that are in A and not in (B or C). So that's region ii. (You'll notice that you didn't have to work out how many are in regions i, iv and viii, but it's good practice!)
Can you complete it now?