Let $A = \{ (x,\,y):y = {e^x},\,x \in R\} $, $B = \{ (x,\,y):y = {e^{ - x}},\,x \in R\} .$ Then

  • A

    $A \cap B = \phi $

  • B

    $A \cap B \ne \phi $

  • C

    $A \cup B = {R^2}$

  • D

    None of these

Similar Questions

Which of the following pairs of sets are disjoint 

$\{ x:x$ is an even integer $\} $ and $\{ x:x$ is an odd integer $\} $

If $X$ and $Y$ are two sets such that $n( X )=17, n( Y )=23$ and $n( X \cup Y )=38$
find $n( X \cap Y )$

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

$D-B$

If $A = \{ x:x$ is a natural number $\} ,B = \{ x:x$ is an even natural number $\} $ $C = \{ x:x$ is an odd natural number $\} $ and $D = \{ x:x$ is a prime number $\} ,$ find $B \cap C$

 

Show that the following four conditions are equivalent:

$(i)A \subset B\,\,\,({\rm{ ii }})A - B = \phi \quad (iii)A \cup B = B\quad (iv)A \cap B = A$