Home
Class 12
MATHS
For each binary operation ** defined bel...

For each binary operation `**` defined below, determine whether `**` is commutative or associative
on Z, define `a**b=a-b`

Text Solution

Verified by Experts

Since `1-2ne2-1, 1**2 ne 2**1`
`therefore ** ` is not commutative
Since `(2-4)-5ne2-(4-5),
`(2**4)**5 ne 2**(4**5)`
`therefore **` is not associative
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

For each binary operation ** defined below, determine whether ** is commutative or associative on Q, define a**b=2^(ab)

For each binary operation ** defined below, determine whether ** is commutative or associative on Q, define a**b=ab+1

For each binary operation ** defined below, determine whether ** is commutative or associative on R-{-1} , define a**b=a/(b+1)

Determine whether * is commutative or associative if a**b=(ab)/6,a,bnotinR

ast ' is a binary operation on R defined as aastb=2ab Determine whether ast is commutative and associative

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

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

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

Let ast be a binary operation on N defined by aastb=HCF of a and b Is ast commutative?

Let A=NtimesN and ' ast ' be the binary operation. On A defined by (a,b)ast(c,d)=(a+c,b+d) . Show that ' ast ' is commutative and associative. Find the identity for ' ast ' on A if any.

A N EXCEL PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Determine whether or not each of the definitions of ** given below giv...

    Text Solution

    |

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

    Text Solution

    |

  3. For each binary operation ** defined below, determine whether ** is co...

    Text Solution

    |

  4. For each binary operation ** defined below, determine whether ** is co...

    Text Solution

    |

  5. For each binary operation ** defined below, determine whether ** is co...

    Text Solution

    |

  6. For each binary operation ** defined below, determine whether ** is co...

    Text Solution

    |

  7. For each binary operation ** defined below, determine whether ** is co...

    Text Solution

    |

  8. For each binary operation ** defined below, determine whether ** is co...

    Text Solution

    |

  9. Consider the binary operation ^^ on the set {1,2,3,4,5} defined by a^^...

    Text Solution

    |

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

    Text Solution

    |

  11. Consider the binary operation ** on the set A= {1,2,3,4,5} given by th...

    Text Solution

    |

  12. Consider the binary operation ** on the set A= {1,2,3,4,5} given by th...

    Text Solution

    |

  13. Let **' be the binary operation on the set {1,2,3,4,5} defined by a**'...

    Text Solution

    |

  14. Let **' be the binary operation on N given by a**'b= L.c.m. of a and b...

    Text Solution

    |

  15. Let **' be the binary operation on N given by a**'b= L.c.m. of a and b...

    Text Solution

    |

  16. Let **' be the binary operation on N given by a**'b= L.c.m. of a and b...

    Text Solution

    |

  17. Let **' be the binary operation on N given by a**'b= L.c.m. of a and b...

    Text Solution

    |

  18. Let **' be the binary operation on N given by a**'b= L.c.m. of a and b...

    Text Solution

    |

  19. Consider an operation ** defined on the set A={1,2,4,8} by a**b=LCM ...

    Text Solution

    |

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

    Text Solution

    |