Home
Class 12
MATHS
Show that ∗ : RxxR->R given by (a ,b)->...

Show that `∗ : RxxR->R` given by `(a ,b)->a+4b^2`is a binary operation.

Text Solution

Verified by Experts

We have,
`∗:R×R→R`, given by
`(a,b)=a+4b^2`
Therefore,
...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 1.4|13 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 1.2|12 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 1.3|14 Videos

  • PROBABILITY

    NCERT|Exercise EXERCISE 13.2|18 Videos

  • SETS

    NCERT|Exercise EXERCISE 1.3|1 Videos

Similar Questions

Explore conceptually related problems

Let *R*R^(rarr) given by (a,b)vec a+4b^(2) is a binary operation.Compute (-5)*2*0)

Let P be the set of all subsets of a given set X. Show that uu:" "P" "xx" "P->P given by (A ," "B) ->Auu B and nn:" "PxxP ->P given by (A ," "B)->AnnB are binary operations on the set P.

Show that the quad vv:R rarr R given by and the and the given by quad (a,b)rarr min{a,b) are binary operations.

Determine whether or not the definition of * On R ,define * by a*b=a+4b^(2) gives a binary operation.In the event that * is not a binary operation give justification of this. Here,Z^(+) denotes the set of all non-negative integers.

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

Determine whether or not the definition of * On R ,define by a*b=ab^(2) gives a binary operation.In the event that * is not a binary operation give justification of this.Here,Z^(+) denotes the set of all non-negative integers.

Show that * on Z^(+) defined by a*b=|a-b| is not binary operation

Which of the following is true? * defined by a*b=(a+b)/2 is a binary operation on Z (b) * defined by a*b=(a+b)/2 is a binary operation on Q (c) all binary commutative operations are associative (d) subtraction is a binary operation on N

Prove that the operation * on the set M={[a00b]:a,b in R-{0}} defined by A*B=AB is a binary operation.

Determine whether or not each of the definition of '**' given below gives a binary operation. In the event that '**' is not a binary operation, given justification for this: (i) On Z^(+) , define '**' by a**b=a-b (ii) On Z^(+) , define '**' by a**b=ab (iii) On R, define '**' by a**b=ab^(2) (iv) On Z^(+) , define '**' by a**b=|a-b| (v) On Z^(+), define '**' by a**b=a .

NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Show that the vv: R ->R given by (a , b)->m a x {a , b}and the ^^: R -...

    Text Solution

    |

  2. Let P be the set of all subsets of a given set X. Show that uu: P xx ...

    Text Solution

    |

  3. Show that ∗ : RxxR->R given by (a ,b)->a+4b^2is a binary operation.

    Text Solution

    |

  4. Show that subtraction and division are not binary operations on N.

    Text Solution

    |

  5. Show that *: Rxx R ->Rgiven by a*b = a +2bis not associative.

    Text Solution

    |

  6. Show that addition and multiplication are associative binary operatio...

    Text Solution

    |

  7. Show that *: R xxR ->Rdefined by a*b = a +2bis not commutative.

    Text Solution

    |

  8. Show that + : R xx R ->R and xx : R xx R ->R are commutative binary ...

    Text Solution

    |

  9. Let Y = {n^2: n in N} in N. Consider f : N ->Yas f(n)=n^2. Show tha...

    Text Solution

    |

  10. Let f : N ->R be a function defined as f(x)=4x^2+12 x+15. Show that f...

    Text Solution

    |

  11. Consider f : N ->N, g : N ->Nand h : N ->Rdefined asf (x) = 2x, g (y) ...

    Text Solution

    |

  12. Consider f : {1, 2, 3} ->{a , b , c}and g : {a , b , c} ->{a p p l e ,...

    Text Solution

    |

  13. Consider functions f and g such that composite gof is defined and is ...

    Text Solution

    |

  14. Are f and g both necessarily onto, if gofis onto?

    Text Solution

    |

  15. Let f : {1, 2, 3}->{a , b , c}be one-one and onto function given by f...

    Text Solution

    |

  16. Let f"":""NvecY be a function defined as f""(x)""=""4x""+""3 , where...

    Text Solution

    |

  17. Let S = {1, 2, 3}. Determine whether the functions f : S->S defi...

    Text Solution

    |

  18. Show that addition, subtraction and multiplication are binary operati...

    Text Solution

    |

  19. Consider the identity function IN : N->N defined as, IN(x)=x for al...

    Text Solution

    |

  20. Let R be a relation on the set A of ordered pairs of positive integer...

    Text Solution

    |