Home
Class 11
MATHS
Show that A nn B=A nn C need not imply B...

Show that `A nn B=A nn C` need not imply `B!=C`

Text Solution

Verified by Experts

let, `A={1,2,3}`
`B={2,3,4}`
`C={2,3,5}`
Then `A cap B={2,3}` and `A cap C ={2,3}` Thus `A cap B=A cap C` event if B is not equal to C
Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|118 Videos

  • SINE AND COSINE FORMULAE AND THEIR APPLICATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|118 Videos

Similar Questions

Explore conceptually related problems

Show that AcapB=AcapC need not imply B=C.

Show that A nn B=A nn B implies A=B

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

Find sets A,B and C such that A nn B,B nn C and A nn C are non empty sets and A nn B nn C=phi

If A, B and C are three sets such that A nn B = A nn C and AuuB = A uu C , then

If A, B and C be sets. Then, show that A nn (B uu C) = (A nn B) uu (A nn C) .

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

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

Let A,B and C be sets such that A nn B sube C and A nn B!=phi. Then which of the following statements is not true?

The probabilities of three events A,B,C are such that P(A)=0.3, P(B)=0.4, P(C)=0.8,P(A nn B)=0.09, P(Ann C) = 0.28, P(A nn B nn C) 0.08 and P(Auu B uu C) leq 0.75.Show that P(B nn C) lies in the interval [0.21, 0.46].

RD SHARMA-SETS-Solved Examples And Exercises
  1. For any two sets A\ a n d\ B ,\ prove that AnnBsubA

    Text Solution

    |

  2. For any two sets A\ a n d\ B ,\ prove that AsubB=>AnnB=A

    Text Solution

    |

  3. Show that A nn B=A nn C need not imply B!=C

    Text Solution

    |

  4. Show that if A subB , then C" "-" "BsubC" "-" "A .

    Text Solution

    |

  5. Prove that Auu (Ann B)= A

    Text Solution

    |

  6. For any two sets, prove that:\ Ann(AuuB)=A

    Text Solution

    |

  7. Find sets A, B and C such that A nnB , B nnC and A nnC are nonempty ...

    Text Solution

    |

  8. For any two sets A\ a n d\ B , prove that AnnB=phi=>AsubeB^(prime)dot

    Text Solution

    |

  9. For any two sets of A and B, prove that: A^(prime)uuB=U=>AsubB

    Text Solution

    |

  10. Is it true that for any sets A and B, P (A) uuP (B) =P(Auu B) ? Just...

    Text Solution

    |

  11. If A and B are any two sets, then prove that (A nn B) uu (A-B)=A

    Text Solution

    |

  12. Show that for any set A and B A = (AnnB)uu(A-B) and Auu(B-A) = (AuuB...

    Text Solution

    |

  13. For any two sets A and B prove the following: Ann(A^(prime)uuB)=AnnB

    Text Solution

    |

  14. For any two sets A and B prove the following: A-(A-B)=AnnB

    Text Solution

    |

  15. For any two sets A and B prove the following: Ann(A^(\ )uuB)'=varphi

    Text Solution

    |

  16. In a class of 35 students, 24 like to play cricket and 16 like to p...

    Text Solution

    |

  17. In a group of 50 people, 35 speak Hindi, 25 speak both English and ...

    Text Solution

    |

  18. Out of 500 car owners investigated, 400 owned car A and 200 owned c...

    Text Solution

    |

  19. A market research group conducted a survey of 2000 consumers and re...

    Text Solution

    |

  20. A survey shows that 63% of the Americans like cheese whereas 76% like ...

    Text Solution

    |