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

Let `**` be the binary operation on N defined by `a" "**" "b" "=" "HdotCdotFdot` of a and b. Is `**` commutative? Is `**` associative? Does there exist identity for this binary operation on N?

Text Solution

Verified by Experts

Let * be a binary operation on `N` given by `a`*`b=H CF (a ,\ b)` for all `a ,\ b in N`
`a`*`b=b`*`a`
`b`*`a=`HCF of b qnd a
`implies a`*`b=b`*`a`
This is commutative.
...
Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSION

    RD SHARMA|Exercise EXAMPLE|5 Videos

  • BINOMIAL DISTRIBUTION

    RD SHARMA|Exercise Solved Examples And Exercises|141 Videos

Similar Questions

Explore conceptually related problems

Let * be the binary operation on N defined by aquad *,b commutative? Is * associative? Does there exist identity for this binary operation on N ?

Commutativity of binary operations

Associativity of binary operations

Consider the binary operation on Z defined by a ^(*)b=a-b . Then * is

Let * be the binary operation on N given by a*b" "=" "LdotCdotMdot of a and b. Find (i) 5" "*" "7," "20" "*" "16 (ii) Is * commutative? (iii) Is * associative? (iv) Find the identity of * in N (v) Which elements of N are invert

Let * be the binary operation on N defined by a*b=HCF of a and b .Does there exist identity for this binary operation on N?

Define an associative binary operation on a set.

Define a commutative binary operation on a set.

Show that the binary operation * on Z defined by a*b=3a+7b is not commutative.

Let * be a binary operation on N given by a*b=LdotCdotM(a , b) for all a , b in N . (i) Find 5*7, 20*16 (ii) Is * commutative?

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let * be a binary operation on N, the set of natural numbers, defined ...

    Text Solution

    |

  2. Let * be a binary operation on N given by a*b=H F C(a ,\ b) for all ...

    Text Solution

    |

  3. Let ** be the binary operation on N defined by a" "**" "b" "=" "Hd...

    Text Solution

    |

  4. Consider the binary operations*: RxxR->R and o: RxxR->R defined as a...

    Text Solution

    |

  5. Let A be a non-empty set and S be the set of all functions from A t...

    Text Solution

    |

  6. Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*...

    Text Solution

    |

  7. Let A be a set having more than one element. Let * be a binary oper...

    Text Solution

    |

  8. Let * be a binary operation on N defined by a*b=1. cdotmdot(a ,\ b)...

    Text Solution

    |

  9. Let '*' be a binary operation on N given by a*b=LdotCdotMdot(a , b) fo...

    Text Solution

    |

  10. Determine whether * on N defined by a*b=1 for all a ,\ b in N is asso...

    Text Solution

    |

  11. Determine whether * on Q defined by a*b=(a+b)/2 for all a ,\ b in Q i...

    Text Solution

    |

  12. Let A be any set containing more than one element. Let * be a binar...

    Text Solution

    |

  13. Check the commutativity and associativity of * on Z defined by a*b=...

    Text Solution

    |

  14. Check the commutativity and associativity of * on N defined by a*b=...

    Text Solution

    |

  15. Check the commutativity and associativity of * on Q defined by a*b=...

    Text Solution

    |

  16. Check the commutativity and associativity of O on Q defined by a\ \...

    Text Solution

    |

  17. Check the commutativity and associativity of o on Q defined by a\ o...

    Text Solution

    |

  18. Check the commutativity and associativity of * on Q defined by a*b=...

    Text Solution

    |

  19. Check the commutativity and associativity of * on Q defined by a*b=...

    Text Solution

    |

  20. Check the commutativity and associativity of * on R defined by a*b=...

    Text Solution

    |