Let $A = \{x : x \in R, |x| < 1\};$ $B = \{x : x \in R, |x - 1| \ge 1\}$ and $A \cup B = R - D,$ then the set $D$ is

If $A$ and $B$ are events of a random experiment with $P(A) = 0.5$,$P(B) = 0.4$ and $P(A \cap B) = 0.3$,then the probability that neither $A$ nor $B$ occurs is

$A$ and $B$ are two sets having $3$ and $6$ elements respectively. Consider the following statements. Statement $(I)$: Minimum number of elements in $A \cup B$ is $6$. Statement $(II)$: Maximum number of elements in $A \cap B$ is $3$. Which of the following is correct?

If $n(X)=700, n(A)=200, n(B)=300,$ and $n(A \cap B)=100$,where $X$ is the universal set and $A$ and $B$ are subsets of $X$,then $n(A' \cap B')=$

Suppose $A_1, A_2, A_3, \dots, A_{30}$ are $30$ sets each having $5$ elements and $B_1, B_2, \dots, B_n$ are $n$ sets each with $3$ elements. Let $\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^n B_j = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s. Then $n$ is equal to:

In a class of $55$ students,$23$ study Mathematics,$24$ study Physics,$19$ study Chemistry,$12$ study Mathematics and Physics,$9$ study Mathematics and Chemistry,$7$ study Physics and Chemistry,and $4$ study all three subjects. Find the number of students who study exactly one subject.