Home
Class 12
MATHS
Let * be the binary operation defined on...

Let * be the binary operation defined on R by a * b = 1 + ab for all a, b `in` R, then the operation * is

A

commutative but not associative

B

associative but not commutative

C

neither commutative nor associative

D

both commutative and associative.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|401 Videos

  • PROBABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|467 Videos

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

Similar Questions

Explore conceptually related problems

Let '*' be the binary operation defined on Q by the rule a * b = (ab)/(4) for all a , b in Q . Is the operaiton * associative?

Fill in the blank: Let R_1 be the set of all reals except 1 and * be the binary operation defined on R_1 as a* b = a + b - ab for all a, b in R_1 . The identity element with respect to the binary operation * is ____________.

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR associative butnot commutative.

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR neither commutative nor associative.

Let '*' be the binary operation defined on Q by the rule a * b = ab^2 for a , b in Q. compute (1*2) *3.

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

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR Commutative but not associative.

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR both commutative and associative.

Let a binary operation '*' be defined on Z by a * b = 2 a + 2b for all a, b in Z. Prove that the given operawtion is commutative but not associative.

let '*' be a binary operation on R defined by a*b = a+b + ab, where a, b inR , then the value of 1*(2*3) is

PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let f:[2, infty) to R be the function defined by f(x)=x^(2)-4x+5, then...

    Text Solution

    |

  2. Let f : R rarr R be defined by f(x) = x^2 +1, then, f^-1(17) and f^-1 ...

    Text Solution

    |

  3. Which of the following function from Z to itself are bijections?

    Text Solution

    |

  4. Let f : R rarr R be the functions defined by f(X) = x^3 + 5, then f^-...

    Text Solution

    |

  5. Let f : R - (3/5) rarr R be defined by f(X) = (3x+2)/(5x-3) , then

    Text Solution

    |

  6. Let f : R rarr Rbe given byf(X) = tan x, then f^-1 (1) is

    Text Solution

    |

  7. Let f:R rarr R be defined by f(x)={{:(2x, xgt3),(x^2,1lexlt3),(3x,xl...

    Text Solution

    |

  8. Let f(x)=ax^(2)+bx+c where a,b,c epsilonR, a!=0. Suppose |f(x)|le1,AA ...

    Text Solution

    |

  9. Which of the following functions is differentiable at x = 0 ?

    Text Solution

    |

  10. Let f: RrarrR be defined f(x) = sin x and g: RrarrR be defined by g...

    Text Solution

    |

  11. Let f: R rarr R be defined as f(X) = 3x. Then

    Text Solution

    |

  12. Let f : X rarr Y and g : Y rarr Z be two invertible functions. Then go...

    Text Solution

    |

  13. Let f (x) = x^2 and g (x) = sqrtx, then

    Text Solution

    |

  14. If f(x) = x+1 And g (X) = 2x, then f (g(x)) is equal to

    Text Solution

    |

  15. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, wh...

    Text Solution

    |

  16. Let f : R rarr R be defined by f(x) = 1/x AA x inR, then f is

    Text Solution

    |

  17. let f : N rarr R be the function defined by f(x) = (2x-1)/(2) and g :...

    Text Solution

    |

  18. The identity element for the binary operation * defined on Q - (0) as ...

    Text Solution

    |

  19. If A = (a,b), then the number of binary operations that can be defined...

    Text Solution

    |

  20. Let * be the binary operation defined on R by a * b = 1 + ab for all a...

    Text Solution

    |