6.2 Interpreting Venn diagrams with three sets


By the end of this section you should be able to:


● understand how to interpret three sets and the Venn diagrams associated with these


So far we have studied sets using two circles (or ovals) in a Venn diagram. However, in this section we are going to explore how to use a Venn diagram when dealing with three sets.


To begin, we will look at how to read and interpret a Venn diagram dealing with three sets. A Venn diagram with three circles is made up of eight diff erent regions.


In set A but not in sets B or C (A\(B∪C))


In sets A and B but not in set C ((A∩B)\C)


A


In set B but not in sets A or C (B\(A∪C))


핌 B


Not in any of the three sets (A∪B∪C)’


C


In sets A and C but not in set B ((A∩C)\B)


In set C, but not in sets A or B (C\(A∪B))


In all three sets (A∩B∩C)


In sets B and C but not in set A ((B∩C)\A)


Worked example 1 A survey was carried out to fi nd out what types of books a group of people liked to read. The results are shown on the Venn diagram. Use the Venn diagram to answer the following questions. (i) How many people participated in the survey? (ii) How many people like to read science fi ction books? (iii) How many people like to read horror books only? (iv) How many people like to read all three types of books? (v) How many people like to read science fi ction and horror books? (vi) How many people do not like to read horror books? (vii) How many people like to read horror and thriller books, but not science fi ction? (viii) If a person was selected at random, what is the probability they would not like to read science fi ction books?


핌


Science fi ction


16 2


14 8 5 20


Thriller Horror 7 9


Solution (i)


(ii)


112


Linking Thinking 2


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