State whether each of the following statements are true or false. If the statement is false, rewrite the given statement 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 $y \in B.$
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 $y$
If two sets $A$ and $B$ have $99$ elements in common, then the number of elements common to the sets $A \times B$ and $B \times A$ is equal to
If $A=\{-1,1\},$ find $A \times A \times A.$
If $A = \{2, 3, 5\}, B = \{2, 5, 6\},$ then $(A -B) × (A \cap B)$ is