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Maths-

General

Easy

Question

If sets $A$ and $B$ are defined as
$A equals open curly brackets open parentheses x comma blank y close parentheses colon y equals fraction numerator 1 over denominator x end fraction comma 0 not equal to x element of R close curly brackets$ ,
$B equals open curly brackets open parentheses x comma blank y close parentheses colon y equals negative x comma blank x element of R close curly brackets$ , 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 $B$ 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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