Question

In a survey of 840 persons, 450 persons believe in morning walk, 300 persons believe in yoga and 200 persons believe both morning walk and yoga. Find the number of persons, who neither believe in morning walk nor yoga.

Answer 1

Let A and B denote the persons who believe in morning walk and yoga, respectively.

Given, total number of persons, n(U)=840

Total number of persons, who believe in morning walk,

n(A)=450

Total number of persons who believe in yoga. n(B)=300 and $n(A\cap B)=200$

We know that $n(A\cup B)-n\left(A\right)+n\left(B\right)-n(A\cap B)$

$n(A\cup B)=450+300-200=550$

$\therefore$ The number of persons who neither believe in morning walk nor yoga.

$n(A\cup B{)}^{\prime }=n(U)-n(A\cap B)=840-550=290$

Hence 290 persons neither believe in morning walk nor yoga.