How do you solve a three circle Venn diagram?

Answer 1

Venn Diagrams are pictorial ways of representing interactions among sets to display information that can be read easily. Each set of given information is designated a circle. Interactions between the sets are shown in the circles' intersections; items common to both sets are found in the intersection whereas otheritems are found outside the intersection. Lets do an example problem to show how such a diagram works:

In a survey of children who saw three different shows at Walt Disney World, the following information was gathered: * 39 children liked The Little Mermaid * 43 children liked 101 Dalmatians * 56 children liked Mickey Mouse * 7 children liked The Little Mermaid and 101 Dalmatians * 10 children liked The Little Mermaid and MickeyMouse * 16 children liked 101 Dalmatians and Mickey Mouse * 4 children liked TheLittle Mermaid, 101 Dalmatians, and Mickey Mouse * 6 children did not like any of the shows Answer the following questions: * How many students were surveyed? * How many liked The Little Mermaid only? * How many liked 101 Dalmatians only? * How many liked Mickey Mouse only?

How to solve:

1. First draw the Venn Diagram

2. Then look at the data you have to work with. Always start with the center of the Venn diagram and work your way out. Fill in the center piece of data.

3. Second, figure and fill in the numbers that go in between two circles.

4. Remember, we have to compensate for the "4" in the center when calculating the numbers which are entered in the middle. Hence, 3 children liked The Little Mermaid and 101 Dalmatians only, 12 children liked 101 Dalmatiansand Mickey Mouse only, and 6 children liked The Little Mermaid and MickeyMouse only.

5. Fill this new data into the Venn Diagram:

6. Our final step in filling out the diagram is to figure out how many children liked only one show. Remember to compensate for both sections of children in the middle. 7. After subtracting necessary values and inserting answers into the Venn Diagram, you should come up with the following diagram:

8. The answers to the last three questions are contained explicitly in the Venn Diagram. 26 children liked The Little Mermaid only, 24 children liked 101 Dalmatians only, and 34 children liked Mickey Mouse only.

9. For the answer to the final question, we need only add up all the children polled. Keep in mind that there were 6 children who did not like any of the shows. Adding all numbers in the diagram plus those that did not belong in the diagram, we find that 115 children were polled in all. 10. The final Venn Diagram would appear as follows: