# 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 :

**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 $K$ can not belong to the set :

Correct Option: , 3

**Solution:**

$n(A \cup B) \geq n(A)+n(B)-n(A \cap B)$

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

$n(A \cup B) \geq 87$

$87 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 89$

Option (3)