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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

A
AB=A
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B
AB=B
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C
AB=ϕ
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D
None of these
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Solution

The correct option is C AB=ϕ
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.
592172_427230_ans.png

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