If sets A and B are defined asB - x - y - y - x - - x - epsilon R - thenA- A - B-BB- A - B -C- A - B - AD- A - B - A

The correct option is B A ∩ B = ϕ x ϵ (A ∩ B)⇒ x ϵ A and x ϵ B i.e. y=1/x and y= x ∴ x ϵ A ∩ B ⇒ x=1/x ⇒ x^2=1 ⇒ x^2= 1, This is not possible for any ...

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Standard XI

Mathematics

Intersection

If sets A and...

Question

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

$A \cap B = A$

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$A \cup B = B$

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$A \cap B = ϕ$

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$A \cup B = A$

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Solution

The correct option is C
$A \cap B = ϕ$

$x ϵ (A \cap B) \Rightarrow x ϵ A a n d x ϵ B i . e . y = \frac{1}{x} a n d y = - x$

$∴ x ϵ A \cap B \Rightarrow - x = \frac{1}{x}$
$\Rightarrow - x^{2} = 1$
$\Rightarrow x^{2} = - 1,$
This is not possible for any real value of $x$ .
$∴ A \cap B = ϕ$

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