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

$A=\{a, e, i, o, u\} B=\{a, b, c\}$

If the sets $A$ and $B$ are defined as $A = \{ (x,\,y):y = {1 \over x},\,0 \ne x \in R\} $ $B = \{ (x,y):y =  – x,x \in R\} $, then

Show that for any sets $\mathrm{A}$ and $\mathrm{B}$, $A=(A \cap B) \cup(A-B)$ and $A \cup(B-A)=(A \cup B).$

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

$B \cup C$

If $A$ and $B$ are disjoint, then $n(A \cup B)$ is equal to