Home
Class 12
MATHS
Show that AcapB=AcapC need not imply B=C...

Show that A`cap`B=A`cap`C need not imply B=C.

Promotional Banner

Topper's Solved these Questions

  • SETS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|31 Videos

  • SETS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|21 Videos

  • SEQUENCES AND SERIES

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|105 Videos

  • STATISTICS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|40 Videos

Similar Questions

Explore conceptually related problems

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

If A,B and C are three sets such that A cap B = A cap C and A cup B = A cup C then

If A, B, C are three sets such that A cup B=A cup C and A cap B=A cap C, then

Find sets A, B and C such that A cap B, B cap C and A cap C are non-empty sets and A cap B cap C= phi .

If A and B are two sets then A cup B=A cap B if and only if

Show that A ∪ B = A ∩ B implies A = B

Let A and B be sets. If A cap X=B cap X= phi and A cup X=B cup X for some set X, show that A=B. (Hints A=A cap (A cup X), B=B cap (B cup X) and use distributive law)

If A={5, 6}, B={4, 5, 6}, C={5, 6, 7} . Show that AtimesA=(BtimesB)cap(CtimesC) .

Check whether A-B= A cap B'

NEW JOYTHI PUBLICATION-SETS-QUESTIONS FROM COMPETITIVE EXAMS
  1. Show that AcapB=AcapC need not imply B=C.

    Text Solution

    |

  2. If A and B are not disjoint sets then n(AcupB) is equal to

    Text Solution

    |

  3. In a city 20 percent of the population travels by car, 50 percent trav...

    Text Solution

    |

  4. Two finite sets have m and n elements. The total number of subsets of ...

    Text Solution

    |

  5. A class has 175 students. The following data shows the number of stude...

    Text Solution

    |

  6. Given n(U)=20, n(A)=12, n(B)=9, n(AcapB)=4, where U is the universal s...

    Text Solution

    |

  7. Two finite sets have m and n elements. The total number of subsets of ...

    Text Solution

    |

  8. If N(a)={an:ninN}, then N(5)capN(7)= (Here N is the set of natural n...

    Text Solution

    |

  9. Two finite sets have m and n elements respectively. The total number o...

    Text Solution

    |

  10. The number of elements in the set {(a,b):2a^(2)+3b^(2)=35, a,binZ}, wh...

    Text Solution

    |

  11. Let A={1,2,3,4}, B={2,4,6}. Then the number of sets C such that AcapBs...

    Text Solution

    |

  12. Let X and Y be the sets of all positive divisors of 400 and 1000 respe...

    Text Solution

    |

  13. In a certain town 25% families own a cell phone, 15% families own a sc...

    Text Solution

    |

  14. Two finite sets A and B have m and n elements respectively. If the tot...

    Text Solution

    |

  15. The shaded region in the figure represents

    Text Solution

    |

  16. If n(A)=8 and n(AcapB)=2, then n((AcapB)'capA) is equal to

    Text Solution

    |

  17. If the set A contains 5 elements, then the number of elements in the p...

    Text Solution

    |

  18. If n(A)=1000, n(B)=500 and if n(AcapB)ge1 and n(AcupB)=p, then

    Text Solution

    |

  19. If n(A)=43, n(B)=51 and n(AcupB)=75, then n((A-B)cup(B-A))=

    Text Solution

    |

  20. If A and B are non-empty sets such that AsupB, then

    Text Solution

    |

  21. Let X={1,2,3,.......,10} and A={1,2,3,4,5}. Then the number of subsets...

    Text Solution

    |