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

$\{2,6,10\}$ and $\{3,7,11\}$ are disjoint sets.

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

$X =\{1,3,5\} \quad Y =\{1,2,3\}$

If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements, and $S$ $\cap \,T$ has $11$ elements, how many elements does $S\, \cup$ $T$ have?

For any sets $\mathrm{A}$ and $\mathrm{B}$, show that

$P(A \cap B)=P(A) \cap P(B).$

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