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Question

Let A={x:xR,|x|<1};
B={x:xR,|x1|1} and

AB=RD, then the set D is


A

{x:1<x2}

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B

{x:1x<2}

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C

{x:1x2}

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D

None of these

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Solution

The correct option is B

{x:1x<2}


Since A={x:xR,|x|<1}
A={x:xR,1<x<1}

and B={x:xR,|x1|1}
B={x:xR,x11 or x11}

={x:xR,x0 or x2}

Now, AB={x:x<1 or x2}

It is given that AB=RD,
using the above information, we can conclude that D={x:xR,1x<2}.


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