Question:
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 $\mathrm{K} \%$ of them are suffering from both ailments, then $\mathrm{K}$ can not belong to the set :
Correct Option: 3,
Solution:
$\mathrm{n}(\mathrm{A} \cup \mathrm{B}) \geq \mathrm{n}(\mathrm{A})+\mathrm{n}(\mathrm{B})-\mathrm{n}(\mathrm{A} \cap \mathrm{B})$
$100 \geq 89+98-n(A \cup B)$
$\mathrm{n}(\mathrm{A} \cup \mathrm{B}) \geq 87$
$87 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 89$
Option (3)
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