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  4. Out of all the patients in a hospital 89 % are found to be suffering from heart ailment and 98 % are suffering from lungs infection. If K % of them are suffering from both ailments, then K can not belong to the set:

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Q. Out of all the patients in a hospital $89 \%$ are found to be suffering from heart ailment and $98 \%$ are suffering from lungs infection. If $K \%$ of them are suffering from both ailments, then $K$ can not belong to the set:

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Solution:

$n ( A \cup B ) \geq n ( A )+ n ( B )- n ( A \cap B )$
$100 \geq 89+98- n ( A \cup B )$
$n ( A \cup B ) \geq 87$
$87 \leq n ( A \cup B ) \leq 89$