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:

Step-by-step solution

Let H and L is set of people suffered from heart ailment and lungs infections respectively. n H = 89 % n L = 98 % n H ∩ L = K % max n ( H ) ,   n L ≤ n H ∪ L ≤ n U Where, U is the universal set. ⇒ 98 ≤ n H ∪ L ≤ 100 ⇒ 98 ≤ n H + n L - n H ∩ L ≤ 100 ⇒ 98 ≤ 89 + 98 - k ≤ 100 ⇒ 0 ≤ 89 - k ≤ 2 ⇒ - 89 ≤ - k ≤ - 87 ⇒ 87 ≤ K ≤ 89