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 $A=\{3,6,9,12,15,18,21\}, B=\{4,8,12,16,20\},$ $C=\{2,4,6,8,10,12,14,16\}, D=\{5,10,15,20\} ;$ find
$D-A$
Let $V =\{a, e, i, o, u\}$ and $B =\{a, i, k, u\} .$ Find $V - B$ and $B - V$
Find the union of each of the following pairs of sets :
$A = \{ x:x$ is a natural number and multiple of $3\} $
$B = \{ x:x$ is a natural number less than $6\} $
If $n(A) = 3$ and $n(B) = 6$ and $A \subseteq B$. Then the number of elements in $A \cap B$ is equal to