8. a) In a group of 60 students, 15 liked maths only, 20 liked science only and 5 did not like
any of two subjects?
(i) How many of them liked at least one subject?
(ii) Find the number of students who liked both the subjects.
(iii) How many of them liked maths?
(iv) How many of them liked science?
Represent the result in a Venn diagram.
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Answer:
(i) no. of students like none of subject = 5
total no. of students= 69
=> no. of students like at least one subject= 60-5
= 55
ii) no. of students like math only = 15
no. of students like science only = 20
total no. of students like only one subject= 35
no. of students like none subject = 5
=> no of students like both the subjects = 60-(35+5) =20
(iii) no. of students like math= 15+ 20
= 35 ( because 15 like math only and 20 like both)
(iv) no. of students like science= 20+20
= 40 ( because 20 like science only and 20 like both )
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