If A and B are two sets defined as A={(x,y):x=yx,y∈R} and B={(x,y):x=y+1x,y∈R} , then
A
A∩B=A
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B
A∩B=B
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C
A∩B=ϕ
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D
None of the above
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Solution
The correct option is CA∩B=ϕ Set A represents all points lying on the line y=x and set B represents all the points on the line x=y+1 Slope of both the lines are same so the lines are parallel. So they have no point in common. ⇒A∩B=ϕ So option C is correct.