Given the sets $A = \{ 1,\,2,\,3\} ,\,B = \{ 3,4\} , C = \{4, 5, 6\}$, then $A \cup (B \cap C)$ is

Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C=\varnothing$

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

$B-D$

If $A=\{1,2,3,4\}, B=\{3,4,5,6\}, C=\{5,6,7,8\}$ and $D=\{7,8,9,10\} ;$ find

$A \cup B$

Show that the following four conditions are equivalent:

$(i)A \subset B\,\,\,({\rm{ ii }})A - B = \phi \quad (iii)A \cup B = B\quad (iv)A \cap B = A$

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