If $A \times B = \{(p, q), (p, r), (m, q), (m, r)\}$,find $A$ and $B$.

If $A = \{x : x^2 - 5x + 6 = 0\}, B = \{2, 4\}, C = \{4, 5\}$,then $A \times (B \cap C)$ is

If $A=\{2,4\}, B=\{3,4,5\}$,then $(A \cap B) \times (A \cup B) =$

If $\left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right)$,find the values of $x$ and $y$.

State whether the following statement is true or false. If the statement is false,rewrite it correctly.
If $A$ and $B$ are non-empty sets,then $A \times B$ is a non-empty set of ordered pairs $(x, y)$ such that $x \in A$ and $y \in B$.

Let $A, B, C$ be three sets such that $n(A \cap B) = n(B \cap C) = n(C \cap A) = n(A \cap B \cap C) = 2$. Then $n((A \times B) \cap (B \times C))$ is equal to -