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Question

If sets A and B are defined as $A equals open curly brackets left parenthesis x comma y right parenthesis colon y equals 1 over x comma 0 not equal to x element of R close curly brackets comma B equals left curly bracket left parenthesis x comma y right parenthesis colon y equals negative x comma x element of R right curly bracket$ , then

$A \cap B = A$
$A \cap B = B$
$A \cap B = ϕ$
None of these

The correct answer is: $A intersection B equals ϕ$

The set A is the set of all points on the hyperbola $x y equals 1$ having its two branches in the first and third quadrants, while the set is the set of all points on $y equals negative x$ which lies in second and four quadrants. These two curves do not intersect.
Hence, $A intersection B equals ϕ$

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