Introduction to Venn Diagrams

According to some examinees, there are several items in the October 2014 Civil Service Exam that requires the use of Venn diagrams, so I will discuss in details how to use Venn diagrams in a series of posts.  In this post, I am going to introduce its concept and its use as layman as possible. I will limit the discussion to the preparation of solving word problems involving Venn diagrams.

Venn diagrams are used to represent logical relations between sets. In word problems involving diagrams, elements of sets are usually people who choose or prefer a particular thing (e.g. color, food, hobbies). For instance, we have two available desserts, biscuits and cookies, and then Abby ate a biscuit and Bella ate a cake. Chubby, being extremely hungry, ate a biscuit and a cake. So, the situation can be represented as follows using a Venn diagram. 

venn diagram

Note that Abby is in the blue area which means that Abby chose biscuits only. Bella is in the red area which means that she chose cookies only. Chubby is in the overlap of the two circles, which means that she chose both. Now, if Debbie is on diet and she didn’t eat any dessert, then the Venn diagram would look like below.

venn diagram 2

The rectangle which includes all four friends, those who ate dessert and those who did not, is called the universal set. Debbie’s name is outside the circles because she did not eat cookies and biscuits.

Now suppose there is a third dessert which is ice cream, and Emma ate all three, then the diagram would look like the one in the next figure.

venn diagrams 1

Suppose Fe, Girlie, and Haidee arrived.  Fe ate ice cream, Girlie ate biscuits and ice cream, and Haidee ate ice cream and cookies, the diagram would look like the one shown in the next figure.

 venn diagrams 2 Once you have learned to use Venn diagrams correctly, it would be easier for you to solve problems involving it. The next step is to read How to Solve Venn Diagram Problems Part 1.

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