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\[A \cap B\]

Answer 1

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:

\[A \cap B\]=\[\varnothing\]