Cardinal Properties

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:

Q. If a relation $R$ is defined on $A=\{1,2,3,4\}$, then which of the following is/are universal relation?

1. $R=\left\{\right(a,b):a+b<10:a,b\in A\}$
2. $R=\left\{\right(a,b):\text{value of}a-b\text{is an integer}:a,b\in A\}$
3. $R=\left\{\right(a,b):\text{value of}\frac{a}{b}\text{is an integer}:a,b\in A\}$
4. $R=\left\{\right(a,b):ab\text{is a real number}:a,b\in A\}$

Q. Two sets such that $n(B-A)=25;n(A-B)=15$ and $n(A\cap B)=10,$ then $n(A\cup B)=$

1. $30$
2. $40$
3. $50$
4. $80$