Home
Class 12
MATHS
Show that the number of binary operation...

Show that the number of binary operations on {1, 2} having 1 as identity and having 2 as the inverse of 2 is exactly one.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTION

    MODERN PUBLICATION|Exercise EXAMPLE|212 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|543 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXAMPLE|13 Videos

Similar Questions

Explore conceptually related problems

Number of binary operations on the set {2, 3} ls :

Show that -a is not the inverse of a in N for the addition operation '+' on N and 1/a is not the inverse of a in N for multiplication operation ‘xx’ on N , for a ne 1 .

Write down the number of commutaive binary operations that can be defined on the set (1,2).

Show that – a is the inverse of a for the addition operation '+' on R and 1/a is the inverse of a ne 0 for the multiplication operation ‘xx’ on R.

Show that the binary operation on the set 'N' given by a * b =1 AA a,b in N is commutative as well as associative.

Show that addition, subtraction and multiplication are binary operations on R, but division is not a binary operation on R. Further, show that division is a binary operation on the set R of nonzero real numbers.

Show that the binary operation '*' defined from N xx N rarr N and given by a*b = 2a + 3b is not commutative.

let '*' be a binary operation on R defined by a*b = a+b + ab, where a, b inR , then the value of 1*(2*3) is

MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Give examples of two one-one function f1 and f2 from R to R such that ...

    Text Solution

    |

  2. Show that if f1 and f2 are one-one maps from r to R, then the product....

    Text Solution

    |

  3. Lert f : X rarr Y be such that fof = f. Show that f is onto if and onl...

    Text Solution

    |

  4. Consider the identity function IN : N rarr N defined as IN (x) = x, fo...

    Text Solution

    |

  5. Find fof^-1 and f^-1 of for the function: f(x) = 1/x, x ne0, also prov...

    Text Solution

    |

  6. Show that the number of binary operations on {1, 2} having 1 as identi...

    Text Solution

    |

  7. Determine whether the following binary operation on the set N is assoc...

    Text Solution

    |

  8. Determine , whether the following binary operation on the set N is ass...

    Text Solution

    |

  9. Consider the binary operation: R xx R rarr R defined as : a** b = |...

    Text Solution

    |

  10. Define a binary operation * on the set A = {0,1,2,3,4,5}, given by a *...

    Text Solution

    |

  11. Given set A = {1,2,3}, then the relation : R = {(1,1),(2,2),(3,3)} is ...

    Text Solution

    |

  12. Give an example of a relation which is symmetric and transitive but no...

    Text Solution

    |

  13. A bijective function is both one-one and onto. (True/False)

    Text Solution

    |

  14. What is the domain of the function f(x) = 1/(x-2)

    Text Solution

    |

  15. If f(x) = {:{(x-2, x<2),(3,x=2),(x+2, x>3):} then, find f(8)

    Text Solution

    |

  16. If a*b = 3a + 4b, then the value of 3*4 is ……….

    Text Solution

    |

  17. If a*b = a/2 + b/3, then the value of 2*3 is …………

    Text Solution

    |

  18. Let A {1,2,3}, for x,y,inA, let R let xRy if and only if x>y. Write d...

    Text Solution

    |

  19. Is -a the inverse of a inN for addition '+' on N?

    Text Solution

    |

  20. Show that 1/a is not the inverse of a in N for multiplication operatio...

    Text Solution

    |