If $A = {(x, y) : y = e^{- x}} a n d B = {(x, y) : y = - x}$ . Then..

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If $A = {(x, y) : y = e^{- x}} & B = {(x, y) : y = - x}$ . Then:
Given $A = {(x, y) : y = e^{- x}} & B = {(x, y) : y = - x}$
Set $A$ element $=$ Set $B$ element
$e^{- x} = - x 1 / e^{x} = - x e^{- x} \neq - 1 / x$
Since the values of $e$ lies in between $2 < e < 3$ for any value of $x$
So $A \cap B = \emptyset$
Hence, $A \cap B = \emptyset$

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