2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Sets

JEE Main & Advanced Mathematics Sets Question Bank Self Evaluation Test - Sets

  • question_answer
    Let X and Y be two non-empty sets such that \[X\cap A=Y\cap A=\phi \] and \[X\cup A=Y\cup A\]for some non-empty set A. Then

    A) X is a proper subset of Y

    B) Y is a proper subset of X

    C) X = Y

    D) X and Y are disjoint sets

    Correct Answer: C

    Solution :

    [c]Suppose \[a\in X\] and \[a\in A\Rightarrow a\in X\cup A\Rightarrow a\in Y\cup A\] \[\Rightarrow a\in Y\,and\,\,a\in A(\therefore X\cup A=Y\cup A)\] \[\Rightarrow a\in Y\cap A\Rightarrow Y\cap A\]is non-empty This contradicts that \[Y\cap A=\phi \] so, \[X=Y\]


You need to login to perform this action.
You will be redirected in 3 sec spinner