Question

In a class of 50 students numbered 1 to 50, all even numbered students opt for Database,
those whose numbers are divisible by 5 opt for Discrete Structure and those whose numbers
are divisible by 7 opt for Programming I. Draw a Venn diagram to show the scenario and give
answer how many opt for none of the three subjects?

Answer 1

Given : In a class of 50 students numbered 1 to 50,

all even numbered students opt for Database,

those whose numbers are divisible by 5 opt for Discrete Structure  

those whose numbers are divisible by 7 opt for Programming I.

To Find : Draw a Venn diagram to show the scenario and give

answer how many opt for none of the three subjects

Solution:

all even numbered students opt for Database,

2 , 4 , 6 _____________, 48 , 50

(25 Students)

D = 25

those whose numbers are divisible by 5 opt for Discrete Structure  

5 , 10 , 15 , __________ . 45,  50  

(10 Students)

S = 10

Common with Even numbers are divisible by 10

10 , 20 , 30 , 40 , 50

(5 Students)

D ∩ S =  5

those whose numbers are divisible by 7 opt for Programming

7 , 14  , ________, 42 , 49

(7 Students)

P = 7

Common with Even numbers are divisible by 14

14 , 28 , 42

D ∩ P =  3

Common with umbers are divisible by 5are  numbers are divisible by 35

35

P ∩ S = 1

as 2 * 5 * 7 = 70

D ∩ S   ∩ P = 0

Choose atleast one of the subject =  D + S + P - D ∩ S -  D ∩ P - P ∩ S  + D ∩ S   ∩ P

= 25 + 10 + 7 - 5  - 3 -  1 + 0

= 33

Choose none = 50 - 33 = 17

Choose none of the subject :

1 , 3 , 9 , 11 , 13 , 17 , 19 , 23 , 27 , 29 , 31 , 33 , 37 , 39 , 41 , 43 , 47

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