Home
Class 12
MATHS
On Z , the set of all integers, a bin...

On `Z` , the set of all integers, a binary operation * is defined by `a*b=a+3b-4` . Prove that * is neither commutative nor associative on `Zdot`

Text Solution

Verified by Experts

* is defined by `a`*`b=a+3b-4` on the set `Z`
Then we have to prove that * is neither associative nor commutative.
Now let `a,b,c in Z`
Then
`(a`*`b)`*`c=(a+3b-4)`*`c`
`(a`*`b)`*`c=a + 3b- 4+3c -4`
`(a`*`b)`*`c= a + 3b + 3c-8 ldots (i)`
...
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

On the set Z of integers a binary operation * is defined by a*b=ab+1 for all a,b in Z Prove that * is not associative on Z

Let * be a binary operation on N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

Let * be a binary operation on Z defined by a*b=a+b-4 for all a,b in Z. show that * is both commutative and associative.

On the set Z of all integers a binary operation * is defined by a*b=a+b+2 for all a,b in Z. Write the inverse of 4.

On Q, the set of all rational numbers a binary operation * is defined by a*b=(a+b)/(2) Show that * is not associative on Q.

Let Z be the set of all integers, then , the operation * on Z defined by a*b=a+b-ab is

On the set Q of all rational numbers if a binary operation * is defined by a*b=(ab)/(5), prove that * is associative on Q.

On the set Z of integers,if the binary operation * is defined by a*b=a+b+2 then find the identity element.

On the set of integers I, if a binary operation 'o' be defined as aob = a - b for every a, b in I , then :

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let S be the set of all real numbers except -1 and let * be an oper...

    Text Solution

    |

  2. Q, the set of all rational number, * is defined by a*b=(a-b)/2 , show ...

    Text Solution

    |

  3. On Z , the set of all integers, a binary operation * is defined by ...

    Text Solution

    |

  4. On the set Q of all rational numbers if a binary operation * is def...

    Text Solution

    |

  5. The binary operation * is defined by a*b=(a b)/7 on the set Q of al...

    Text Solution

    |

  6. On Q , the set of all rational numbers a binary operation * is defi...

    Text Solution

    |

  7. Let S be the set of all rational number except 1 and * be defined ...

    Text Solution

    |

  8. Let S be the set of all rational number except 1 and * be defined ...

    Text Solution

    |

  9. If * defined on the set R of real numbers by a*b=(3a b)/7 , find the i...

    Text Solution

    |

  10. Find the identity element in set Q^+ of all positive rational numbers ...

    Text Solution

    |

  11. If * is defined on the set R of all real numbers by a*b=sqrt(a^2+b^2) ...

    Text Solution

    |

  12. Let S be a non-empty set and P(s) be the power set of set S. Find the ...

    Text Solution

    |

  13. Find the identity element in the set I^+ of all positive integer...

    Text Solution

    |

  14. Find the identity element in the set of all rational numbers except ...

    Text Solution

    |

  15. If the binary operation * on the set Z is defined by a*b=a+b-5, then ...

    Text Solution

    |

  16. On the set Z of integers, if the binary operation * is defined by a...

    Text Solution

    |

  17. On Q, the set of all rational numbers, a binary operation * is defined...

    Text Solution

    |

  18. Let * be a binary operation on set Q-[1] defined by a*b=a+b-a b for al...

    Text Solution

    |

  19. Show that the binary operation * on A=R-{-1} defined as a*b=a+b+a b fo...

    Text Solution

    |

  20. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

    Text Solution

    |