Problem Solving With Venn Diagrams

Problem Solving With Venn Diagrams-84
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.He went on to repeat the work by giving names to the students, showing the benefit of using math and ignoring such details!

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.He went on to repeat the work by giving names to the students, showing the benefit of using math and ignoring such details!

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.

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.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 Salt Bay circle should have 3 people in it, but there are already two people in the part of the circle that intersects with the other circle, so there is just one person in the part of the Salt Bay circle that is not within the other circle.Similarly, there will be 2 people in the Punta de las Cuevas circle that are not in the part that overlaps the Salt Bay circle. This is typical of many more complicated problems, in that the key idea is subtraction.Twelve belong to the computer club, and eight belong to the photography club. This question is listed in a section introducing proportions.I can't figure out a way to come up with the correct answer or use a proportion to solve it.When he asked how many had been to Punta de las Cuevas, four children raised their hands.When he asked how many had been to Salt Bay, three raised their hands.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.

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