Problem Solving With Venn Diagrams

Problem Solving With Venn Diagrams-18
We’ll start with a simple problem involving two sets, from 1996: How Many are in the Group? Jackson polled the class to see how many students had been to one or both of the nearby state parks.He found that everyone in Katie's group had been to at least one of the parks.

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In a town 85% of the people speak Tamil, 40% speak English and 20% speak Hindi.

Also 32% speak Tamil and English, 13% speak Tamil and Hindi and 10% speak English and Hindi, find the percentage of people who can speak all the three languages.

The real trick to word problems is trying to turn the words into equations.

Let's summarize what we have in a table for easy reference: Number of students Place who have been there Punta de las Cuevas 4 Salt Bay 3 Both 2 Neither 0 We have several ways of looking at this but probably the easiest is a logical argument.

Similarly, for Salt Bay we have three students who have gone, but two also went to Punta de las Cuevas so we must remove those two from the three who have been. of students who have only been to Salt Bay Thus only one student has gone to only Salt Bay.

To get the final answer we note that the sum of the students who have only been to Punta de las Cuevas, plus those who have only been to Salt Bay, plus those who have been to both must be the total in the group.

Some of these are very easy, some much harder, and solved by different techniques.

Let’s look at a few of them, including some where the meaning is easy to get wrong.

Number of people who use Television :n(T) = 115Number of people who use Radio : n(R) = 110Number of people who use Magazine : n(M) = 130Number of people who use Television and Magazinesn (Tn M) = 85Number of people who use Television and Radio :n(Tn R) = 75Number of people who use Radio and Magazine :n(Rn M) = 95Number of people who use all the three : n(Tn Rn M) = 70 At a certain conference of 100 people there are 29 Indian women and 23 Indian men.

Out of these Indian people 4 are doctors and 24 are either men or doctors. Find the number of women doctors attending the conference.


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