Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank space:
$2 \dots A$

Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$,then the value of $m \times n$ is

Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C = \varnothing$.

For two sets $A$ and $B$,$A \cup B = A$ if and only if

The number of subgroups of the group $(Z_{5}, +_{5})$ is

Which of the following pairs of sets are equal? Justify your answer.
$A = \{ n : n \in \mathbb{Z} \text{ and } n^2 \le 4 \}$ and $B = \{ x : x \in \mathbb{R} \text{ and } x^2 - 3x + 2 = 0 \}$.