If $A = \{ a,\,b\} ,\,B = \{ c,\,d\} ,\,C = \{ d,\,e\} ,\,$ then $\{ (a,\,c),\,(a,\,d),\,(a,\,e),\,(b,\,c),\,(b,\,d),\,(b,\,e)\} $ is equal to

Let $A = \{1, 2, 3, 4, 5\}; B = \{2, 3, 6, 7\}$. Then the number of elements in $(A × B) \cap (B × A)$ is

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

$A \times(B \cap C)$

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

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

If two sets $A$ and $B$ are having $99$ elements in common, then the number of elements common to each of the sets $A \times B$ and $B \times A$ are