If sets A and B are defined as A = { (x,,y):y = {1 over x},,0 ne x ∈ R} B = { (x,y):y = - x,

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1.Set Theory

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

A

$A \cap B = A$

B

$A \cap B = B$

C

$A \cap B = \phi $

D

None of these

Solution

(c) Since $\,y = {1 \over x},\,y = – x$ meet when $ – x = {1 \over x}$ ==> ${x^2} = – 1$, which does not give any real value of $x.$

Hence, $\,A \cap B = \phi $.

Standard 11

Mathematics

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