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

If $n(A)=4$ and $n(B)=2$,then the number of subsets of the set $A \times B$ each having at least $3$ elements is:

If the set $A$ has $3$ elements and the set $B = \{3, 4, 5\},$ then find the number of elements in $(A \times B).$

The Cartesian product $A \times A$ has $9$ elements,among which are found $(-1, 0)$ and $(0, 1)$. Find the set $A$ and the remaining elements of $A \times A$.

Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\}$. Verify that $A \times (B \cap C) = (A \times B) \cap (A \times C)$.

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 $y \in B$.