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Question

If $A equals open curly brackets open parentheses x comma y close parentheses colon y to the power of 2 end exponent equals x semicolon x comma y element of R close curly brackets$ and
$B equals open curly brackets open parentheses x comma y close parentheses colon y equals open vertical bar x close vertical bar semicolon x comma y element of R close curly brackets comma$ then

(a) $A \cap B = ϕ$
$A \cap B$ is a singleton set
$A \cap B$ contains two elements only
$A \cap B$ contains three elements only

The correct answer is: $A intersection B$ contains three elements only

Clearly, $y to the power of 2 end exponent equals x$ and $y equals vertical line x vertical line$ intersect at $open parentheses 00 close parentheses comma left parenthesis 11 right parenthesis$ and $left parenthesis negative 1 comma negative 1 right parenthesis$ . Hence, option ((d) is correct

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