Home
Class 12
MATHS
Let S=(0,1,2,3,4,) and * be an operation...

Let `S=(0,1,2,3,4,)` and * be an operation on S defined by `a*b=r` , where`r` is the least non-negative remainder when `a+b` is divided by 5. Prove that * is a binary operation on S.

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

Let S={0,1,2,3,4} and * be an operation on S defined by a*b=r , where r is the last non-negative remainder when a+b is divided by 5. Prove that * is a binary operation on S.

Let S={1,\ 2,\ 3,\ 4} and * be an operation on S defined by a*b=r , where r is the least non-negative remainder when product is divided by 5. Prove that * is a binary operation on Sdot

On the set W of all non-negative integers * is defined by a*b=a^b . Prove that * is not a binary operation on Wdot

Consider the set S={1,\ 2,\ 3,\ 4} . Define a binary operation * on S as follows: a*b=r , where r is the least non-negative remainder when a b is divided by 5. Construct the composition table for * on Sdot

Is * defined by a * b=(a+b)/2 is binary operation on Z.

Let * be a binary operation defined by a * b=3a+4b-2 . Find 4*5.

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

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

Let * be a binary operation o Q defined by a*b= (ab)/4 for all a,b in Q ,find identity element in Q

Let * be a binary operation on set of integers I, defined by a*b=2a+b-3. Find the value of 3*4.

RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Find dy/dx if 3x-4y=sinx

    Text Solution

    |

  2. Let S={0,1,2,3,4} and * be an operation on S defined by a*b=r , where ...

    Text Solution

    |

  3. Let S=(0,1,2,3,4,) and * be an operation on S defined by a*b=r , where...

    Text Solution

    |

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

    Text Solution

    |

  5. Let S={a+sqrt(2)b : a , b in Z}dot Then prove that an operation * on ...

    Text Solution

    |

  6. Let A be a set having more than one element. Let '*' be a binary ope...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

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

    Text Solution

    |

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

    Text Solution

    |

  15. Let * be a binary operation o Q defined by a*b= (ab)/4 for all a,bin Q...

    Text Solution

    |

  16. If the binary operation o is defined on the set Q^+ of all positive ra...

    Text Solution

    |

  17. Let S={a+sqrt(2)\ b\ : a ,\ b in Z}dot Then, prove that an operati...

    Text Solution

    |

  18. Let S={1,\ 2,\ 3,\ 4} and * be an operation on S defined by a*b=r , wh...

    Text Solution

    |

  19. Let S=(0,1,2,3,4,) and * be an operation on S defined by a*b=r , where...

    Text Solution

    |

  20. Show that the operation vv and ^^ on R defined as avvb= Maximum of ...

    Text Solution

    |