If $aN = \{ ax : x \in N \}$,then the set $3N \cap 7N$ is equal to .....$N$.

$A$ and $B$ are two subsets of set $S = \{1, 2, 3, 4\}$ such that $A \cup B = S$. Find the number of ordered pairs $(A, B)$.

Let $A = \{x : x \in N \text{ and } x \text{ is a multiple of } 2\}$,$B = \{x : x \in N \text{ and } x \text{ is a multiple of } 5\}$,and $C = \{x : x \in N \text{ and } x \text{ is a multiple of } 10\}$. Describe the set $A \cap (B \cup C)$.

Domain of the function $f(x) = {\left[ {{{\log }_{10}}\left( {\frac{{5x - {x^2}}}{4}} \right)} \right]^{1/2}}$ is

If $A = \{2, 3, 4, 8, 10\}, B = \{3, 4, 5, 10, 12\}, C = \{4, 5, 6, 12, 14\}$,then $(A \cap B) \cup (A \cap C)$ is equal to

If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$,then: