If the sets $A$ and $B$ are defined as $A = \{ (x,\,y):y = {e^x},\,x \in R\} $; $B = \{ (x,\,y):y = x,\,x \in R\} ,$ then
$B \subseteq A$
$A \subseteq B$
$A \cap B = \phi $
$A \cup B = A$
Find the union of each of the following pairs of sets :
$A = \{ x:x$ is a natural number and $1\, < \,x\, \le \,6\} $
$B = \{ x:x$ is a natural number and $6\, < \,x\, < \,10\} $
If $A$ and $B$ are any two sets, then $A \cap (A \cup B)$ is equal to
Is it true that for any sets $\mathrm{A}$ and $\mathrm{B}, P(A) \cup P(B)=P(A \cup B) ?$ Justify your answer.
If $A =$ [$x:x$ is a multiple of $3$] and $B =$ [$x:x$ is a multiple of $5$], then $A -B$ is ($\bar A$ means complement of $A$)
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
$B-D$