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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    Let \[A=[x:x\in R,\,|x|\,<1]\,;\] \[B=[x:x\in R,\,|x-1|\ge 1]\] and \[A\cup B=R-D,\] then the set D is

    A) \[[x:1<x\le 2]\]

    B) \[[x:1\le x<2]\]

    C) \[[x:1\le x\le 2]\]

    D) None of these

    Correct Answer: B

    Solution :

    \[A=[x:x\in R,\,-1<x<1]\] \[B=[x:x\in R:x-1\le -1\] or \[x-1\ge 1]\]     = \[[x:x\in R:x\le 0\text{ or }x\ge 2]\] \[\therefore \]\[A\cup B=R-D\], where D = \[[x:x\in R,\,1\le x<2]\].


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