Home
Class 12
MATHS
Define a commutative binary operation...

Define a commutative binary operation on a set.

Text Solution

Verified by Experts

Let `S` be a non-empty set, and `star` said to be a binary operation on `S`, if `a star b` is defined for all `a, b in S`. In other words, `star` is a rule for any two elements in the set `S`.
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

Define a binary operation on a set.

Define an associative binary operation on a set.

Commutativity of binary operations

Let A be a non-empty set and S be the set of all functions from A to itself. Prove that the composition of functions 'o' is a non-commutative binary operation on Sdot Also, prove that 'o' is an associative binary operation on Sdot

The number of commutative binary operations that can be defined on a set of 2 elements is (a) 8 (b) 6 (c) 4 (d) 2

State whether the following statements are true or false.Justify.(i) For an arbitrary binary operation on a set N,a*a=a a a N( ii) If . is a commutative binary operation on N, then a*(b*c)=(c*b)*a

A binary operation is chosen at random from the set of all binary operations on a set A containing n elements.The probability that the binary operation is commutative,is

Define identity element for a binary operation defined on a set.

Discuss the commutativity and associativity of the binary operation * on R defined by a*b=(ab)/(4) for all a,b in R

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. On the set Z of all integers a binary operation * is defined by a*b...

    Text Solution

    |

  2. Define a binary operation on a set.

    Text Solution

    |

  3. Define a commutative binary operation on a set.

    Text Solution

    |

  4. Define an associative binary operation on a set.

    Text Solution

    |

  5. Write the total number of binary operations on a set consisting of ...

    Text Solution

    |

  6. Write the identity element for the binary operation * defined on th...

    Text Solution

    |

  7. Let * be a binary operation, on the set of all non-zero real number...

    Text Solution

    |

  8. Write the inverse of 5 under multiplication modulo 11 on the set {1...

    Text Solution

    |

  9. Define identity element for a binary operation defined on a set.

    Text Solution

    |

  10. Write the composition table for the binary operation multiplication...

    Text Solution

    |

  11. Write the composition table for the binary operation multiplication ...

    Text Solution

    |

  12. For the binary operation multiplication modulo 5\ (xx5) defined on ...

    Text Solution

    |

  13. Write the composition table for the binary operation xx5 (multiplic...

    Text Solution

    |

  14. A binary operation * is defined on the set R of all real numbers by...

    Text Solution

    |

  15. Let +6 (addition modulo 6) be a binary operation on S={0,\ 1,\ 2,\ ...

    Text Solution

    |

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

    Text Solution

    |

  17. If the binary operation * on the set Z of integers is defined by...

    Text Solution

    |

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

    Text Solution

    |

  19. Let * be a binary operation on set of integers I , defined by a*b=2...

    Text Solution

    |

  20. If a*b=a^2+b^2, then the value of (4*5)*3 is a*b=a^2+b^2, then the val...

    Text Solution

    |