​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? 

Dear Student

We are going to use Venn diagram concept for better understanding.

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

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