Out of 14 people, twelve said that it was not the case that they watched television but didn t listen - Maths - Sets Relations and Functions

Question

​Out of 14 people, twelve said that it was not the case that
they watched television but didn’t listen to the radio Also,
for nine people it is not the case that they do not watch T V and
do not listen to the radio Finally, seven people either watch
television or listen to the radio but do not do both How many
people watch T V and how many listen to the radio?

Aman Rajput · Accepted Answer

Dear Student

We are going to use Venn diagram concept for better
understanding

(T∩R')'=12 ⇒(T'∪R)=12(T'∩R')'=9   ⇒(T∪R)=9only T+only R = 7  ⇒n(T)+n(R)-2(T∩R)=7Total 14 , i
e
 n(U)=14Now , Three conditions to draw on venn diagram
We get on solvingonly T=2only R=6T∩R=1n(T)=3n(R)=7
Regards