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 = \{ (x,\,y):y = {e^x},\,x \in R\} $, $B = \{ (x,\,y):y = {e^{ - x}},\,x \in R\} .$ Then
If $X = \{ {4^n} - 3n - 1:n \in N\} $ and $Y = \{ 9(n - 1):n \in N\} ,$ then $X \cup Y$ = . . . . .
State whether each of the following statement is true or false. Justify you answer.
$\{a, e, i, o, u\}$ and $\{a, b, c, d\}$ are disjoint sets.
If $A$ and $B$ are two sets such that $A \subset B$, then what is $A \cup B ?$