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

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 $A, B$ and $C$ are any three sets, then $A \times (B  \cup C)$ is equal to

If $n(A) = 4$, $n(B) = 3$, $n(A \times B \times C) = 24$, then $n(C) = $

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

Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\} .$ Find

$(A \times B) \cup(A \times C)$