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Question
If \[A = \left\{ \left( x, y \right) : y = \frac{1}{x}, 0 \neq x \in R \right\}\]and\[B = \left\{ \left( x, y \right) : y = - x, x \in R \right\}\] then write\[A \cap B\]
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Solution
We have:
\[A = \left\{ \left( x, y \right) : y = \frac{1}{x}, 0 \neq x \in R \right\}\]
\[\left( 1, 1 \right), \left( 2, \frac{1}{2} \right), \left( 3, \frac{1}{3} \right), \left( 4, \frac{1}{4} \right)\]And, \[B = \left\{ \left( x, y \right) : y = - x, x \in R \right\}\]
=\[\left\{ \left( 1, - 1 \right), \left( 2, - 2 \right), \left( 3, - 3 \right), \left( 4, - 4 \right), . . . \right\}\]
Thus, we get:
\[A \cap B\]=\[\varnothing\]
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