Home
Class 12
MATHS
Let ** be a binary operation on the set ...

Let `**` be a binary operation on the set Z of integers as `a**b=a+b+1`. Then find the identity element:

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|86 Videos
  • PROBABILITY

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|318 Videos
  • THREE DIMENSTIONAL GEOMETRY

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|97 Videos

Similar Questions

Explore conceptually related problems

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a+ab . Is the binary operation commutative and associative ?

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a^2+b^2 . Is the binary operation commutative and associative ?

Let ** be a binary operation on the set Q of rational numbers as follows a**b=(a-b)^2 . Is the binary operation commutative and associative ?

*be a binary operation on Q,defined as a**b=(3ab)/5 Find the identity element of *if any.

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a-b . Check whether * is commutative and associative

ast ' is a binary operation on R defined as aastb=2ab Find the identity element if exists.

A={1,2,3,4,6},ast is a binary operation on A is defined as aastb=HCF of a and b. Find the identity element.

ast ' be a binary operation on NxxN defined as (a,b)ast(c,d)=(ac,bd) Find the identity element of ast if any

Let ast be a binary operation defined on NtimesN by (a,b)ast(c,d)=(a+c,b+d) Find the identity element for ast if it exists.

* be a binary operation on Q,defined as a**b=(3ab)/5 .Show that *is commutative.

A N EXCEL PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Consider an operation ** defined on the set A={1,2,4,8} by a**b=LCM ...

    Text Solution

    |

  2. Let ast be a binary operation on N defined by aastb=HCF of a and b I...

    Text Solution

    |

  3. Let ** be a binary operation on the set Q of rational numbers as follo...

    Text Solution

    |

  4. Let ** be a binary operation on the set Q of rational numbers as follo...

    Text Solution

    |

  5. Let ** be a binary operation on the set Q of rational numbers as follo...

    Text Solution

    |

  6. Let ** be a binary operation on the set Q of rational numbers as follo...

    Text Solution

    |

  7. Consider the binary operation ast on the set R of real numbers, define...

    Text Solution

    |

  8. Determine whether or not each of the definitions of ** given below giv...

    Text Solution

    |

  9. Find which of the following of the operations given above has identity...

    Text Solution

    |

  10. Find which of the following of the operations given above has identity...

    Text Solution

    |

  11. Find which of the following of the operations given above has identity...

    Text Solution

    |

  12. Find which of the following of the operations given above has identity...

    Text Solution

    |

  13. Let ** be a binary operation on the set Z of integers as a**b=a+b+1. T...

    Text Solution

    |

  14. Let A=NtimesN and ast be a binary operation on A defined by (a,b)...

    Text Solution

    |

  15. State whether the following statements are true or false. Justify For...

    Text Solution

    |

  16. State whether the following statements are true or false. Justify If ...

    Text Solution

    |

  17. Consider a binary operation ** on N defined as a**b=a^3+b^3. Choose th...

    Text Solution

    |

  18. Let f:RrarrR be defined as f(x) = 10x+7 Find the function g:RrarrR s...

    Text Solution

    |

  19. Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 if...

    Text Solution

    |

  20. If f:RrarrR is defined by f(x) = x^2-3x+2, find f(f(x))

    Text Solution

    |