If $A, B, C$ be three sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$, then

Find the union of each of the following pairs of sets :

$A=\{1,2,3\}, B=\varnothing$ 

If $A=\{3,6,9,12,15,18,21\}, B=\{4,8,12,16,20\},$ $C=\{2,4,6,8,10,12,14,16\}, D=\{5,10,15,20\} ;$ find

$A-D$

Let $\mathrm{X}=\{\mathrm{n} \in \mathrm{N}: 1 \leq \mathrm{n} \leq 50\} .$ If $A=\{n \in X: n \text { is a multiple of } 2\}$ and $\mathrm{B}=\{\mathrm{n} \in \mathrm{X}: \mathrm{n} \text { is a multiple of } 7\},$ then the number of elements in the smallest subset of $X$ containing both $\mathrm{A}$ and $\mathrm{B}$ is

If $A=\{3,5,7,9,11\}, B=\{7,9,11,13\}, C=\{11,13,15\}$ and $D=\{15,17\} ;$ find

$B \cap C$

If $A=\{3,5,7,9,11\}, B=\{7,9,11,13\}, C=\{11,13,15\}$ and $D=\{15,17\} ;$ find

$\left( {A \cap B} \right) \cap \left( {B \cup C} \right)$