Question

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
AB=A
B
AB=B
C
AB=ϕ
D
None of these
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.

2
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