Home
Class 11
MATHS
Show that A ∪ B = A ∩ B implies A = B...

Show that `A ∪ B = A ∩ B` implies `A = B`

Promotional Banner

Topper's Solved these Questions

  • SETS

    NCERT GUJARATI|Exercise EXERCISE 1.1|33 Videos

  • SETS

    NCERT GUJARATI|Exercise EXERCISE 1.2|21 Videos

  • SEQUENCES AND SERIES

    NCERT GUJARATI|Exercise Miscellaneous Exercise On Chapter 9|31 Videos

  • STATISTICS

    NCERT GUJARATI|Exercise Miscellaneous Exercise On Chapter 15|7 Videos

Similar Questions

Explore conceptually related problems

Show that A ∩ B = A ∩ C need not imply B = C .

Show that if A ⊂ B , then C – B ⊂ C – A .

If A and B are any two sets, prove that P(A) = P(B) implies A = B.

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C . Show that B = C .

Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

Let A , B and C be the sets such that A uu B=A uu C and A nn B = A nn C . show that B=C

If A, B and C be sets. Then, show that, A cap (B cup C) = (A cap B) cup (A cap C) .

Assume that P ( A ) = P ( B ) . Show that A = B

If A and B are subsets of the universal set cup , then show that, A sub B iff A cup B = B

NCERT GUJARATI-SETS-MISCELLANEOUS EXERCISE ON CHAPTER 1
  1. Show that A ∪ B = A ∩ B implies A = B

    Text Solution

    |

  2. Decide, among the following sets, which sets are subsets of one and a...

    Text Solution

    |

  3. In each of the following, determine whether the statement is true or f...

    Text Solution

    |

  4. In each of the following, determine whether the statement is true or f...

    Text Solution

    |

  5. In each of the following, determine whether the statement is true or f...

    Text Solution

    |

  6. In each of the following, determine whether the statement is true or f...

    Text Solution

    |

  7. In each of the following, determine whether the statement is true or f...

    Text Solution

    |

  8. In each of the following, determine whether the statement is true or f...

    Text Solution

    |

  9. Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C....

    Text Solution

    |

  10. Show that if A ⊂ B, then C – B ⊂ C – A.

    Text Solution

    |

  11. Assume that P ( A ) = P ( B ). Show that A = B

    Text Solution

    |

  12. Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B )?...

    Text Solution

    |

  13. Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ...

    Text Solution

    |

  14. Using properties of sets, show that A ∪ ( A ∩ B ) = A

    Text Solution

    |

  15. Using properties of sets, show that A ∩ ( A ∪ B ) = A.

    Text Solution

    |

  16. Show that A ∩ B = A ∩ C need not imply B = C.

    Text Solution

    |

  17. Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some s...

    Text Solution

    |

  18. Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty s...

    Text Solution

    |

  19. In a survey of 600 students in a school, 150 students were found to be...

    Text Solution

    |

  20. In a group of students, 100 students know Hindi, 50 know English and 2...

    Text Solution

    |

  21. In a survey of 60 people, it was found that 25 people read newspaper H...

    Text Solution

    |