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Question

If sets A and B are defined as A={(x, y):y=1x, 0xR} and B={(x, y):y=x, xR}, then
  1. AB=B
  2. AB=A
  3. AB=ϕ
  4. None of these

A
AB=A
B
AB=ϕ
C
AB=B
D
None of these
Solution
Verified by Toppr

y=1xxy=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 AB=ϕ.
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