If the sets A and B are defined as
A={(x,y):y=1x, x ∈ R−{0}}
B={(x,y):y=−x, x ∈ R}, then
A∩B=∅
It is given that
A={(x,y):y=1x, x ∈ R−{0}}
B={(x,y):y=−x, x ∈ R}
As A∩B is set of ordered pairs of (x,y) for which curves y=1x and y=−x intersects each other.
For the points of intersection, we have −x = 1x
⇒ x2=−1,
which does not give any real value of x, so there is no point of intersection.
Hence, A∩B=∅.