If sets A and B are defined as A={(x,y):y=1x,0≠x∈R} and B={(x,y):y=−x,x∈R}, then
A
A∩B=A
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
A∩B=B
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
A∩B=ϕ
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Noneofthese
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is CA∩B=ϕ y=1x⇒xy=1. ∴A is the set of all points on the rectangular hyperbola. xy=1 with branches in I and III quadrants, y=−x represents a line with slope ′−1′ and c equal to ′0′. ∴B is the set of all points on this line. Since the graphs of xy=1 and y=−x are non-intersecting, we have A∩B=ϕ.