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∩B=B
A∩B=A
A∩B=ϕ
Noneofthese
A
A∩B=A
B
A∩B=ϕ
C
A∩B=B
D
Noneofthese
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Solution
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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.
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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