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Question

If the sets A and B are defined as

A={(x,y):y=1x, x R{0}}

B={(x,y):y=x, x R}, then


A

AB=A

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B

AB=B

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C

AB=

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D

None of these

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Solution

The correct option is C

AB=


It is given that

A={(x,y):y=1x, x R{0}}

B={(x,y):y=x, x R}


As AB is set of ordered pairs of (x,y) for which curves y=1x and y=x intersects each other.

For the points of intersection, we have x = 1x
x2=1,

which does not give any real value of x, so there is no point of intersection.

Hence, AB=.


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