(A) The set $A$ contains all $x$ such that $f(x) = 0$.The set $B$ contains all $x$ such that $g(x) = 0$.The intersection $A \cap B$ contains all $x$ s

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(A) The set $A$ contains all $x$ such that $f(x) = 0$.The set $B$ contains all $x$ such that $g(x) = 0$.The intersection $A \cap B$ contains all $x$ such that $f(x) = 0$ $AND$ $g(x) = 0$.If $f(x) = 0$ and $g(x) = 0$,then the sum of their squares must also be zero,i.e.,${[f(x)]^2} + {[g(x)]^2} = 0$.Thus,$A \cap B = \{x : {[f(x)]^2} + {[g(x)]^2} = 0\}$.

Class 11 Mathematics Set Theory Venn Diagram and Operation on Sets

Medium

If $A = \{x : f(x) = 0\}$ and $B = \{x : g(x) = 0\}$,then $A \cap B$ will be

A
${[f(x)]^2} + {[g(x)]^2} = 0$
B
$\frac{f(x)}{g(x)} = 0$
C
$\frac{g(x)}{f(x)} = 0$
D
None of these

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Set Theory

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Venn Diagram and Operation on Sets

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DifficultJEE MAIN 2019

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If $A = \{x : f(x) = 0\}$ and $B = \{x : g(x) = 0\}$,then $A \cap B$ will be

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If the sets $A$ and $B$ are defined as $A = \{ (x, y) : y = \frac{1}{x}, x \in R, x \neq 0 \}$ and $B = \{ (x, y) : y = -x, x \in R \}$,then:

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