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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    If the sets A and B are defined as\[A=\{(x,\,y):y=\frac{1}{x},\,0\ne x\in R\}\]\[\bigcup\limits_{i=1}^{30}{{{A}_{i}}}=\bigcup\limits_{j=1}^{n}{{{B}_{j}}}\], then

    A) \[A\cap B=A\]

    B) \[A\cap B=B\]

    C) \[A\cap B=\varphi \]

    D) None of these

    Correct Answer: C

    Solution :

    Since \[\,y=\frac{1}{x},\,y=-x\] meet when \[-x=\frac{1}{x}\] Þ \[{{x}^{2}}=-1\], which does not give any real value of x. Hence, \[\,A\cap B=\varphi \].


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