Need help with Venn Diagram

ethan

New member
Joined
Oct 30, 2012
Messages
7
I have a Venn diagram to complete and am stuck. The sets are A for winged, A' for not winged B for less and 1/2", B' for not less than 1/2" C for more than one color and C' for not more than one color. The question is for sets of insects. I have my three circle Venn diagram all set, with the number of insects in A, B and C, but am unsure where to place the insects that fall into the A' B' and C' category. The question is how many insects in the collection and I have that equalled out to 60. I am just unsure whether I should put the A' insects in the same part of the circle as the straight A on the diagram or have it ouside the circle?
 
It would be helpful to upload and post your diagram. Also, please type the exercise wording as given. Cheers :cool:
 
I have a Venn diagram to complete and am stuck. The sets are A for winged, A' for not winged B for less and 1/2", B' for not less than 1/2" C for more than one color and C' for not more than one color. The question is for sets of insects. I have my three circle Venn diagram all set, with the number of insects in A, B and C, but am unsure where to place the insects that fall into the A' B' and C' category. The question is how many insects in the collection and I have that equalled out to 60. I am just unsure whether I should put the A' insects in the same part of the circle as the straight A on the diagram or have it ouside the circle?

OK, Got it. Here's the excercise:

The sets are
A for winged, A' for not winged
B for less and 1/2", B' for not less than 1/2"
C for more than one color, C' for not more than one color

2 insects are in A,B, and C
7 insects are in A and C
6 insects are in C & B
5 insects are in A & C
12 insects are in B and A' and C'
9 insects are in A and B' and C'
14 insects are in C and B' & A'
5 insects are in A', B' and C'

Are there 54 insects in the colelction?

I have 60 insects in the collection, since there are no instructions listing what rule an insect needs to be in to be in the collection.


So in the three circle Venn, I have A on top, B & C in the bottom circles.

I have 9 in A, 5 in AB, 12 in B, 6 in BC, 14 in C, 7 in AC and 2 and 5 in the center. These numbers include the A', B' and C' category of insects since I don't know where else to put them.

Is this correct?

Thanks!
 
That is how the teacher said to do it. She gave us a handout with the three circle Venn diagram and said to use tally marks for the number of insects in it.
 
This is off the teacher's web page for the homework:

This Week's: POW 7 - Venn Diagram



  • Have the appropriate labels or titles in each section
  • Use tallies fill in the diagram
  • Are there 54 in total?
64357460.jpgThis is the handout she gave for the Venn diagram
 
Last edited:
Please confirm that you understand the following.

If set A is represented by blue regions, then set A' is represented by red regions.

InsecticideA.jpgInsecticideA'.jpg
 
Sorry, yes. There are two on top on one on bottom. I was not looking at the hand out when I types the statement previously
 
Hello, ethan!

There are three sets: \(\displaystyle A,B,C.\)

2 insects are in \(\displaystyle A \cap B \cap C\)
7 insects are in \(\displaystyle A \cap B\)
6 insects are in \(\displaystyle B \cap C\)
5 insects are in \(\displaystyle A \cap C\)
9 insects are in \(\displaystyle A \cap B' \cap C'\)
12 insects are in \(\displaystyle B \cap A' \cap C'\)
14 insects are in \(\displaystyle C \cap B' \cap A'\)
5 insects are in \(\displaystyle A' \cap B' \cap C'\)

Are there 54 insects in the collection? . Yes!

If you read the information correctly,
the Venn diagram should look like this:


Code:
      *-----------------------------------*
      |                                   |
      |             *-------*             |
      |            /    A    \            |
      |           /           \           |
      |          /             \          |
      |         *       9       *         |
      |         |               |         |
      |       *-+-----*   *-----+-*       |
      |      /  |      \ /      |  \      |
      |     /   *       X       *   \     | 
      |    /     \  5  / \ 3   /     \    | 
      |   *       \   *   *   /       *   |
      |   |        \  | 2 |  /        |   | 
      |   | B       *-+---+-*       C |   | 
      |   |     12    |   |     14    |   | 
      |   *           * 4 *           *   | 
      |    \           \ /           /    |
      |     \           X           /     | 
      |      \         / \         /      | 
      |       *-------* - *-------*       | 
      |                 5                 |
      *-----------------------------------*



Note that set \(\displaystyle A\) is the region inside circle \(\displaystyle A.\)


Code:
[SIZE=2][SIZE=3]
      *-------------------*
      |                   | 
      |      *-----*      | 
      |     /:::::::\     | 
      |    /:::::::::\    | 
      |   *:::: A ::::*   | 
      |   |:::::::::::|   |
      |   |:::::::::::|   |
      |   *:::::::::::*   |
      |    \:::::::::/    |
      |     \:::::::/     |
      |      *-----*      | 
      |                   | 
      *-------------------*[/SIZE][/SIZE]



And \(\displaystyle A'\) is the region outside circle \(\displaystyle A.\)


Code:
[SIZE=3][SIZE=3]
      *-------------------*
      |:::::::::::::::::::| 
      |: A' :*-----*::::::| 
      |:::::/       \:::::| 
      |::::/    A    \::::| 
      |:::*           *:::| 
      |:::|           |:::|
      |:::|           |:::|
      |:::*           *:::|
      |::::\         /::::|
      |:::::\       /:::::|
      |::::::*-----*::::::| 
      |:::::::::::::::::::| 
      *-------------------*[/SIZE][/SIZE]

But it is understood to be there.
Usually, we don't shade it in.
 
Thank you! Sorry if it seems a dumb question, but how do you get 54 insects? I got 60.
 
How do you get 54 insects?

9 + 5 + 3 + 2 + 12 + 4 + 14 + 5 = 54

Do your numbers match soroban's?

Note: In my prior reply, I described A' as the red region to differentiate in terms of the circles. The entire area outside of the three circles could also be red.
 
Top