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

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

$A \times(B \cap C)=(A \times B) \cap(A \times C)$

Let $A, B, C$ are 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 × B) \cap  (B × C)) $ is equal to -

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

$A \times(B \cup C)$

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