Question 63

In a housing society of 100 members, 64 people read the Hindu newspaper and 80 read the Times of India. If 6 members do not read any paper, how many members read the Hindu but not the Times of India?

Solution

Let H and T be the sets of Hindu and Times of India readers. $$n(H \cup T)=100-6=94=n(H)+n(T)-n(H \cap T)=80+64-x$$. Hence $$x=50$$. $$n(H)=n(H \cap T')+ n(H \cap T)=y+50=64$$. Hence $$y=14.$$

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