Consider the following relations :

$(1) \,\,\,A - B = A - (A \cap B)$

$(2) \,\,\,A = (A \cap B) \cup (A - B)$

$(3) \,\,\,A - (B \cup C) = (A - B) \cup (A - C)$

which of these is/are correct

Show that $A \cap B=A \cap C$ need not imply $B = C$

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

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

$A \cup B \cup C$

If $X$ and $Y$ are two sets such that $X \cup Y$ has $18$ elements, $X$ has $8$ elements and $Y$ has $15$ elements ; how many elements does $X \cap Y$ have?

State whether each of the following statement is true or false. Justify you answer.

$\{2,3,4,5\}$ and $\{3,6\}$ are disjoint sets.