Home
Class 11
MATHS
Prove(AcapB)^(c)=A^(c)uuB^(c)....

Prove`(AcapB)^(c)=A^(c)uuB^(c)`.

Text Solution

Verified by Experts

The correct Answer is:
`=A^(c)uuB^(c)`,
Promotional Banner

Topper's Solved these Questions

  • SETS

    MODERN PUBLICATION|Exercise EXERCISE 1 (a) (Short Answer Type Questions)|7 Videos

  • SETS

    MODERN PUBLICATION|Exercise EXERCISE 1 (b) (Short Answer Type Questions)|7 Videos

  • SETS

    MODERN PUBLICATION|Exercise CHAPTER TEST 1|12 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • STATISTICS

    MODERN PUBLICATION|Exercise Chapter Test|7 Videos

Similar Questions

Explore conceptually related problems

(a) If U= {1,2,3,……, 10} ,A = { 1,2,3,4,5}, B= {1,3,5,7,9} , C {2,4,8,10}, verify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) (iii) A-B=AcapB^(c) (iv) Acap(BuuC)=(AcapB)uu(AcapC) . (b) If U={1,2,3,4,5,6,7,8,9}, A={2,4,6,8} and B= {2,3,5,7}. Veify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) .

Let U={1,2,3,4,5,6,7,8,9},A = {2,4,6,8} and B={2,3,5,7} . Verify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) .

Prove that : (i) (AuuBuuC)^(c)=A^(c)capB^(c)capC^(c) (ii) (AcapBcapC)^(c)=A^(c)uuB^(c)uuC^(c) (iii) (AuuB)=(A-B)uu(B-A)uu(AcapB) .

Prove that : (i) (AuuBuuC)^(c)=A^(c)capB^(c)capC^(c) (ii) (AcapBcapC)^(c)=A^(c)uuB^(c)uuC^(c) .

If A and B are two events such that P(A)=(4)/(7), P(AnnB)=(3)/(28) and the conditional probability P((A)/(A^(c )uuB^(c ))) (where A^(c ) denotes the compliment of the event A) is equal to lambda , then the value of (26)/(lambda) is equal to

Prove that : (i) A^(c) - B^(c)=B-A (ii) B^(c)-A^(c)=A-B .

Prove that A^(c)-B^(c)=B-A .

Prove the following : (i) A-B=A-(AcapB) (ii) U-(U-A)=(A^(c))^(c)=A , where U is the universal set.

If (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b), then prove that (a^(a))(b^(c))(c^(c))=1

If (Ina)/((b-c)) =(Inb)/((c-a))=(Inc)/((a-b)) ,Prove that a^(b+c).b^(c+a).c^(a+b)=1

MODERN PUBLICATION-SETS -Frequently Asked Questions
  1. If A={1,2,3},B={4,5,6} and C=(7,8,9} , verify that : Auu(BcapC)=(A...

    Text Solution

    |

  2. Let U={1,2,3,4,5,6,7,8,9},A = {2,4,6,8} and B={2,3,5,7} . Verify that ...

    Text Solution

    |

  3. Prove(AcapB)^(c)=A^(c)uuB^(c).

    Text Solution

    |

  4. If A nnn B' = phi then prove that A = AnnnB and hence show that Asube...

    Text Solution

    |

  5. If AuuB=AcapB, prove that A=B.

    Text Solution

    |

  6. If A and B are any two sets ,prove that : (i) A-B=AcapB^(c) (ii) ...

    Text Solution

    |

  7. Show that : (AuuB)-(AcapB)=(A-B)uu(B-A).

    Text Solution

    |

  8. If A , B and C are any three sets , then prove that : Acap(B-C)=(Ac...

    Text Solution

    |

  9. Prove the following : (i) AsubBhArrB^(c)subA^(c) (ii) BsubArArrA...

    Text Solution

    |

  10. Prove the following : (i) A-B=A-(AcapB) (ii) U-(U-A)=(A^(c))^(...

    Text Solution

    |

  11. Shade the following : (i) A^(c)cap(BuuC) (ii) A^(c)cap(C-B) in ...

    Text Solution

    |

  12. If X and Y are two sets such that has 18 elements, X has 8 elements ...

    Text Solution

    |

  13. A and B are two sets containing repectively m(1)andm(2) elements. I...

    Text Solution

    |

  14. If set A and B has 3 and 6 elements respecitvely. Find the maximum and...

    Text Solution

    |

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

    Text Solution

    |

  16. Suppose A1,A2….. A(30) are thirty sets each having 5 elements and B1B2...

    Text Solution

    |

  17. If A , B and C are three non - empty finite sets such that n (A) =19 ,...

    Text Solution

    |

  18. Out of 20 members in a family , 11 like to take tea and 14 like coffee...

    Text Solution

    |

  19. There are 20 students in a Chemistry class and 30 students in a Physic...

    Text Solution

    |

  20. In a survey of 400 students in a school, 100 were listed as taking app...

    Text Solution

    |