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In a survey of 200 people, it is observed that 125 of them use Television, 120 of them use Radio and 135 of them use Mobile. But, it is noted that 70 of them use both Television and Radio, 85 of them use both Radio and Mobile, 75 of them use both Television and Mobile, and 50 of them use all the three devices. Find the following using the Venn diagram.
 
(i) How many of them use only Television and Radio, not Mobile?
 
(ii) How many of them use only Radio and Mobile, not Television?
 
(iii) How many of them use only Television and Mobile, not Radio?
 
(iv) How many of them use only Television?
 
(v) How many of them use only Radio?
 
(vi) How many of them use only Mobile?
 
Solution:
 
Let us say, A, B and C represent the sets of people who use Television, Radio, and Mobile, respectively.
 
Total number of people = n(U) = 200
 
Number of people use Television = n(A) = 125
 
Number of people use Radio = n(B) = 120
 
Number people use Mobile = n(C) = 135
 
Number of people use Television and Radio = n(A \cap B) = 70
 
Number of people use Radio and Mobile = n(B \cap C) = 85
 
Number of people use Television and Mobile = n(A \cap C) = 75
 
Number of people use all the three = n(A \cap B \cap C) = 50
 
Cardinality_2.svg
 
From the diagram:
 
(i) Number of people use only Television and Radio, but not a Mobile = 20
 
(ii) Number of people use only Radio and Mobile, but not a Television = 35
 
(iii) Number of people use only Television and Mobile, but not a Radio = 25
 
(iv) Number of people use only Television = 30
 
(v) Number of people use only Radio = 15
 
(vi) Number of people use only Mobile = 25