Home
Class 12
MATHS
Let ast be a binary operation on the set...

Let `ast` be a binary operation on the set Q of rational numbers defined by `aastb=frac(ab)(3)`. Check whether `ast` is commutative and associative?

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    MAXIMUM PUBLICATION|Exercise EXAMPLE|144 Videos
  • THREE DIMENSIONAL GEOMETRY

    MAXIMUM PUBLICATION|Exercise EXAMPLE|136 Videos

Similar Questions

Explore conceptually related problems

Consider the binary operation ast on the set R of real numbers, defined by aastb=a b /4 Show that ast is commutative and 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 ' is a binary operation on the set Q of rational numbers as follows, aastb=a+ab Check whether the binary operation are commutative and associative. Also find the identify element if exists.

Let ' ast ' is a binary operation on the set Q of rational numbers as follows, aastb=(a-b)^2 Check whether the binary operation are commutative and associative. Also find the identify element if exists.

Let ' ast ' is a binary operation on the set Q of rational numbers as follows, aastb=a-b Check whether the binary operation are commutative and associative. Also find the identify element if exists.

Let ' ast ' is a binary operation on the set Q of rational numbers as follows, aastb=a^2+b^2 Check whether the binary operation are commutative and associative. Also find the identify element if exists.

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a+ab . Is the binary operation commutative and associative ?

Let ** be a binary operation on the set Q of rational numbers as follows a**b=(a-b)^2 . Is the binary operation commutative and associative ?

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a^2+b^2 . Is the binary operation commutative and associative ?

Let ast be a binary operation on the set Q of rational numbers by aastb=2a+b . Find 2ast(3ast4) and (2ast3)ast4 .

MAXIMUM PUBLICATION-RELATIONS AND FUNCTIONS-EXAMPLE
  1. Consider the function f:NtoN, given by f(x)=x^3. Show that the functio...

    Text Solution

    |

  2. The given table shows an operation aston A={p,q} (Figure) Is ast a ...

    Text Solution

    |

  3. The given table shows an operation aston A={p,q} (Figure) Is ast co...

    Text Solution

    |

  4. Let R be relation defined on A={1,2,3} by R={(1,3),(3,1),(2,2)} is

    Text Solution

    |

  5. Find fog and gof if f(x)=abs(x+1) and g(x)=2x-1

    Text Solution

    |

  6. Let ast be a binary operation defined on NtimesN by (a,b)ast(c,d)=(a+c...

    Text Solution

    |

  7. If R={(x,y):x,y inZ,x-y inZ}, then the relation R is

    Text Solution

    |

  8. Let ast be a binary operation on the set Q of rational numbers by aast...

    Text Solution

    |

  9. Let f:RtoR,g:RtoR be two one-one functions. Check whether gof is one-o...

    Text Solution

    |

  10. A function f:XtoY is onto if range of f=……….

    Text Solution

    |

  11. Let f:{1,3,4}to{3,4,5} and g:{3,4,5}to{6,8,10} be functions defined by...

    Text Solution

    |

  12. Let Q be the set of Rational numbers and 'ast' be the binary operation...

    Text Solution

    |

  13. Let Q be the set of Rational numbers and 'ast' be the binary operation...

    Text Solution

    |

  14. Show that aast(bastc)=(aastb)astc,AAa,b,c inQ.

    Text Solution

    |

  15. Let R be the relation on the set N of natural numbers given by R={(a...

    Text Solution

    |

  16. If f(x)=8x^3 and g(x)=x^(1/3), find g(f(x)) and f(g(x))

    Text Solution

    |

  17. Let ast be a binary operation on the set Q of rational numbers defined...

    Text Solution

    |

  18. Let f(x)=frac(x-1)(x-3),xne3 and g(x)=frac(x-3)(x-1),xne1 be two fun...

    Text Solution

    |

  19. Let f(x)=frac(x-1)(x-3),xne3 and g(x)=frac(x-3)(x-1),xne1 be two fun...

    Text Solution

    |

  20. Let f(x)=frac(x-1)(x-3),xne3 and g(x)=frac(x-3)(x-1),xne1 be two fun...

    Text Solution

    |