De Morgan's Law

Q. In an examination, out of $100$ students, $75$ passed in English, $60$ passed in Mathematics and $45$ passed in both English and Mathematics. The number of students who passed in none of the two subjects, is
(Assume all students gave both the exams)

1. $5$
2. $10$
3. $20$
4. $40$

Q. Let $A=\{x:2<|x|\le 5\text{and}x\in Z\}$ and $B$ be the set of values of $a$ for which the equation $||x-1|+a|=4$ can have real solutions. Then $n(A\cap B)$ is

Q. In a examination, $45\%$of the candidates have passed in English, $40\%$ have passed in Hindi, while $30\%$ have passed in both the subjects. find the total number of candidates, if $90$ of them have failed in both the subjects.

1. $100$
2. $200$
3. $50$
4. None of the above

Q. Let $n\left(U\right)=700$, $n\left(A\right)=200$, $n\left(B\right)=300$ and $n(A\cap B)=100$, Then $n(A^C\cap B^C)=$

1. $100$
2. $300$
3. $500$
4. $450$

Q.

If the number of elements in each of universal set, set A and set B are represented as $n\left(U\right)$, $n\left(A\right)$, $n\left(B\right)$ respectively, then the number of elements that are not in set A and not in set B is given by ___.

1. $n\left(AU{B}^{\prime }\right)$

2. $n\left(\right(A\cap B{)}^{\prime })$

3. $n\left(U\right)-n(A\cap B)$

4. $n\left(U\right)-n(A\cup B)$