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

JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    If A and B are two sets, then \[A\cup B=A\cap B\] iff

    A) \[A\subseteq B\]

    B) \[B\subseteq A\]

    C) \[A=B\]

    D) None of these\[\]

    Correct Answer: C

    Solution :

    Let\[x\in A\Rightarrow x\in A\cup B\],  \[[\because A\subseteq A\cup B]\] Þ \[x\in A\cap B\], \[[\because A\cup B=A\cap B]\] Þ \[x\in A\]and \[x\in B\] Þ \[x\in B\], \\[A\subseteq B\] Similarly, \[x\in B\]Þ \[x\in A\], \\[B\subseteq A\] Now \[A\subseteq B,\,\,B\subseteq A\] Þ \[A=B\].


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