Home
Class 12
MATHS
Let P(A) b the power set of non-empty se...

Let P(A) b the power set of non-empty set A. A binary operation `**` is defined on P(A) as `X**Y=XcapY` for all `X,YinP(A)`. Detemine the identity element In P(A). Prove that A is the only invertible element in P(A).

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise MCQs|5 Videos

  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise Integar Answer Type|5 Videos

  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3 (Short Answer Type Questions)|40 Videos

  • ARCHIVE

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|13 Videos

  • BINOMIAL DISTRUTION

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

Let P(C ) be the power set of non-empty set C. A binary operation ** is defined on P(C ) as A**B=(A-B)cup(B-A) for all A,BinP(C ) . Prove that Phi is the identity element for ** on P(C ) and A is invertible for all AinQQ_(0) .

Let A={0,1,2,3,4,5} be a given set, a binary operation @ is defined on A by a@b=ab(mod6) for all a,bin A. Find the identity element for @ in A . Show that 1 and 5 are the only invetible elements in A.

Let P(A) be the power set of a non-empty set A and a binary operation @ on P(A) is defined by X@Y=XcupY for all YinP(A). Prove that, the binary operation @ is commutative as well as associative on P(A). Find the identity element w.r.t. binary operation @ on P(A). Also prove that Phi inP(A) is the only invertible element in P(A).

On the set Q^+ of all positive rational numbers if the binary operation * is defined by a * b = 1/4ab for all a,b in Q^+ find the identity element in Q^+ .

Let * be a binary operations on Z and is defined by , a * b = a + b + 1, a, bin Z . Find the identity element.

On the set QQ^(+) of all positive rational numbers if the binary operation ** is defined by a**b=(1)/(4)ab for all a,binQQ^(+) , find the identity element in QQ^(+) . Also prove that any element in QQ^(+) is invertible.

*' is an operation defined on Z set of all integers as a*b = a+b-2 for all a,b in z . Find identity element of *'

Find the identity element of the binary operation ** on ZZ defined by a**b=a+b+1 for all a,binZZ .

Let A= Q xxQ . Let * be a binary operation Defined by: (a,b)*(c,d)= (ac,ad +b). Then (i) find the identity element of (A,*)

Let A be a set of 3 elements. The number of differentity binary operations can be defined A is…

CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Long Answer Type Questions)
  1. Construct the composition table for the binary operation multiplicatio...

    Text Solution

    |

  2. A binary operation ** on NN is defined by a**b=L.C.M.(a,b) for all a,...

    Text Solution

    |

  3. Let P(A) b the power set of non-empty set A. A binary operation ** is ...

    Text Solution

    |

  4. A binary operation ** is defined in QQ(0), the set of all non-zero rat...

    Text Solution

    |

  5. Let P(C ) be the power set of non-empty set C. A binary operation ** ...

    Text Solution

    |

  6. Let A=Ncup{0}xxNNcup{0}, a binary operation ** is defined on A by. (a,...

    Text Solution

    |

  7. Let A={0,1,2,3,4,5} be a given set, a binary operation @ is defined on...

    Text Solution

    |

  8. Let A=NNxxNN, a binary operation ** is defined on A by (a,b)**(c,d)=(a...

    Text Solution

    |

  9. Find the values of (i) 4+(6)2 (ii) 7+(5)7 (iii) 5+(8)2 (iv) 3xx(7)...

    Text Solution

    |

  10. Let M(2)(x)d={:{((x,x),(x,x)):},x inRR} be the set of 2xx2 singular ma...

    Text Solution

    |

  11. Prepare the composition table for addition modulo 6 (+(6)) on A={0,1,2...

    Text Solution

    |

  12. Prepare the composition table for multiplication modulo 6 (xx(6)) on A...

    Text Solution

    |

  13. A binary operaiton ^^ on the set A={1,2,3,4,5} is defined by a^^b=min(...

    Text Solution

    |

  14. Let S={1,omega,omega^(2)} be the set of cube roots of unity. Prepare t...

    Text Solution

    |

  15. Prepare the composition table for multiplication (xx) on the set of fo...

    Text Solution

    |

  16. Complete the following nultiplication table so as to define a commutat...

    Text Solution

    |

  17. A binary operation @ is defined on the set A={0,1,2,3,4,5} as follows:...

    Text Solution

    |

  18. An operation ** is defined on the set A={1,2,3,4} as follows: a**b,ab(...

    Text Solution

    |

  19. Let A={1,-1} be the set of square roots of unity. Considering multipli...

    Text Solution

    |

  20. Let ** be the binary defined on the set S={1,2,3,4,5,6} by a**b=r whe...

    Text Solution

    |