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 $
$A \cup B = A$
If $X = \{ {4^n} - 3n - 1:n \in N\} $ and $Y = \{ 9(n - 1):n \in N\} ,$ then $X \cup Y$ = . . . . .
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?
Let $A$ and $B$ be two sets. Then
Let $A = \{ (x,\,y):y = {e^x},\,x \in R\} $, $B = \{ (x,\,y):y = {e^{ - x}},\,x \in R\} .$ Then
If $A = \{2, 3, 4, 8, 10\}, B = \{3, 4, 5, 10, 12\}, C = \{4, 5, 6, 12, 14\}$ then $(A \cap B) \cup (A \cap C)$ is equal to