Out of all patients in a hospital 89, % are found to be suffering from heart ailment and 98, % are s

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1.Set Theory

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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 :

A

$\{79,81,83,85\}$

B

$\{84,86,88,90\}$

C

$\{80,83,86,89\}$

D

$\{84,87,90,93\}$

(JEE MAIN-2021)

Solution

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

$100 \geq 89+98-\mathrm{n}(\mathrm{A} \cap \mathrm{B})$

$\mathrm{n}(\mathrm{A} \cap \mathrm{B}) \geq 87$

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

Standard 11

Mathematics

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