Problem Solving With Venn Diagrams

Problem Solving With Venn Diagrams-1
Sometimes when I know the correct answer I can work backwards to solve it, but I can't do that with this problem. This sort of problem is often solved using a Venn diagram.

Sometimes when I know the correct answer I can work backwards to solve it, but I can't do that with this problem. This sort of problem is often solved using a Venn diagram.

Let’s look at one more example with two sets, this one using a table rather than a Venn diagram.

This is from 2009: Alternate Solution Path to Venn Diagram Problem There are 30 students in a math class. I know that the correct answer (according to the book) is 13. I have either 10 or 7 as my answers, not knowing if the "both club" members are included already in the listed number of members.

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.

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.Puzzles involving two or three properties of people or objects, commonly solved by Venn diagrams, are popular with teachers, and perhaps not so popular with students!Several have asked about them recently, leading me to catalog our past answers about them, to find the most useful examples to point to.So: 2 1 2 = 5 Thus there are 5 students in the group.You may notice that the work here is identical; it just took more words, in the absence of pictures!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.In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games.Find the total number of students in the group In a college, 60 students enrolled in chemistry,40 in physics, 30 in biology, 15 in chemistry and physics,10 in physics and biology, 5 in biology and chemistry. Find how many are enrolled in at least one of the subjects.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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