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Maths-

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Easy

Question

Let $A equals open curly brackets open parentheses x comma y close parentheses colon y equals e to the power of x end exponent comma x element of R close curly brackets comma$
$B equals open curly brackets open parentheses x comma y close parentheses colon y equals e to the power of negative x end exponent comma x element of R close curly brackets.$ Then,

$A \cap B = ϕ$
$A \cap B \neq ϕ$
$A \cup B = R^{2}$
None of these

The correct answer is: $A intersection B not equal to ϕ$

The set $A$ consists of all points on $y equals e to the power of x end exponent$ and the set $B$ consists of points on $y equals e to the power of negative x end exponent$ , these two curves intersect at (0, 1). Hence, $A intersection B$ consists of a single point

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