If A - A - x - y - y -1- x - 0- x - R and B - x - y - y - x - x - R - then write A - B

Let zϵ A ∩ B ⇒ z ϵ A and z ϵ B ⇒ z ϵ{ (x,y):y= 1/x, 0 ≠ x ϵ R } and z ϵ{ (x,y): y= x, x ϵ R } ⇒ z ϵ{ (x,y): x = 1/x, 0 ≠ x ϵ R } ⇒ z ϵ{ (x,y): x^2= 1, ...

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Byju's Answer

Standard XII

Mathematics

Intersection

If A = A = x ...

Question

If A = $A = {(x, y) : y = \frac{1}{x}, 0 \neq x ϵ R}$ and B = { $(x, y) : y = - x, x ϵ R$ }, then write $A \cap B$ .

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Solution

Let $z ϵ A \cap B$

$\Rightarrow z ϵ A a n d z ϵ B$

$\Rightarrow z ϵ {(x, y) : y = \frac{1}{x}, 0 \neq x ϵ R} a n d$

$z ϵ {(x, y) : y = - x, x ϵ R}$

$\Rightarrow z ϵ {(x, y) : - x = \frac{1}{x}, 0 \neq x ϵ R}$

$\Rightarrow z ϵ {(x, y) : x^{2} = - 1, x ϵ R}$

$\Rightarrow z ϵ {}$

Therefore $A \cap B$ is an empty set.

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If A = A={(x,y):y=1x,0≠xϵR} and B = {(x,y):y=−x,xϵR}, then write A∩B.

Let zϵA∩B ⇒z ϵA and z ϵB ⇒z ϵ{(x,y):y=1x,0≠x ϵR} and z ϵ{(x,y):y=−x,x ϵ R} ⇒z ϵ{(x,y):−x=1x,0≠x ϵ R} ⇒z ϵ{(x,y):x2=−1,x ϵ R} ⇒z ϵ{ } Therefore A∩B is an empty set.

If A = $A = {(x, y) : y = \frac{1}{x}, 0 \neq x ϵ R}$ and B = { $(x, y) : y = - x, x ϵ R$ }, then write $A \cap B$ .