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Q.
In a town of $840$ persons, $450$ persons read Hindi, $300$ read English and $200$ read both. Then the number of persons who read neither is
Sets
Solution:
Let $H$ and $E$ denote the number of persons who read Hindi and English newspaper respectively.
Given, total number of persons, $n(U) = 840$
Total number of persons who read Hindi newspaper,
$n(H) = 450$
Total number of persons who read English newspaper,
$n(E) =300$
and $n(H \cap E) = 200$
$\because n(H \cup E) = n(H) + n(E) - n(H \cap E) = 550$
$\therefore \,$ The number of persons who read neither of the newspaper
$ = n(\bar{H} \cap \bar{E}) = n(U) - n(H \cup E) = 290$