Home
Class 12
MATHS
Show that the binary operation * on Z ...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

  • BINOMIAL DISTRIBUTION

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

Similar Questions

Explore conceptually related problems

Determine whether the binary operation ** on R defined by a ** b = |a -b| is commutative. Also, find the value of (-3) ** 2.

Determine whether the binary operation * on R defined by aast b =|a-b| is commutative. Also, find the value of (-3)^(ast) 2 .

Examine whether the binary operation ** defined on R by a**b=a b+1 is commutative or not.

For the binary operation * on Z defined by a*b= a+b+1 the identity element is

Let A be any set containing more than one element. Let * be a binary operation on A defined by a*b=b for all a ,\ b in Adot Is * commutative A ?

Show that the binary operation * on A=R-{-1} defined as a*b=a+b+a b for all a ,bA is commutative and associative on Adot Also find the identity element of * in A and prove that every element of A is invertible.

Show that the binary operation * on A=R-{-1} defined as a*b=a+b+a b for all a ,bA is commutative and associative on Adot Also find the identity element of * in A and prove that every element of A is invertible.

Let A be a set having more than one element. Let * be a binary operation on A defined by a*b=a for all a ,\ b in Adot Is * commutative or associative on A ?

Let * be a binary operation on R defined by a*b=a b+1 . Then, * is commutative but not associative associative but not commutative neither commutative nor associative (d) both commutative and associative

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

RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Check the commutativity and associativity of * on N defined by a*b=g...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. On the set Z of integers a binary operation * is defined by a*b=a b+...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. On the set Q of all rational numbers if a binary operation * is defi...

    Text Solution

    |

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

    Text Solution

    |

  9. On Q , the set of all rational numbers a binary operation * is defin...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Find the identity element in the set I^+ of all positive integers ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |