Home
Class 12
MATHS
Consider the binary operations *:" "RxxR...

Consider the binary operations `*:" "RxxR ->R` and `o:" "R" "xx" "R->R` defined as `a*b|a-b|` and `a" "o" "b" "=" "a , AA""""a ," "b in R` . Show that * is commutative but not associative, o is associative but not commutative. Further, show that `AAa

Text Solution

Verified by Experts

The correct Answer is:
NO
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.4|13 Videos

  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

  • VECTOR ALGEBRA

    NCERT GUJARATI|Exercise Miscellaneous Exercise on chapter 10|18 Videos

Similar Questions

Explore conceptually related problems

** be a binary operation on R defined by a"*"b = (a)/(4)+b/(7) , a,b inR . Show that ** is not commutative and associative.

If ** be binary operation defined on R by a**b = 1 + ab, AA a,b in R . Then the operation ** is (i) Commutative but not associative. (ii) Associative but not commutative . (iii) Neither commutative nor associative . (iv) Both commutative and associative.

A binary operation ** be defined on the set R by a**b = a+b +ab . Show that ** is commutative, and it is also Associative.

** be binary operation defined on a set R by a**b=a+b-(ab)^2 . Show that ** is commutative, but it is not associative. Find the identity element for ** .

Let ** be the binary operation on Q define a**b = a + ab . Is ** commutative ? Is ** associative ?

Prove that binary operation on set R defined as a**b = a +2b does not obey associative rule.

L A = NxxN and ** be the binary operation on A defined by (a,b) "*" (c,d) = (a+c,b+d) Show that ** is commutative and associative . Find the identity element for ** on A , if any.

Let ** be a binary operation on the set Q of rational numbers as follows : a "*" b = a^(2) +b^(2) Find which of the binary operations are commutative and which are associative.

Show that **: RxxR rarr R defined by a^(**) b = a + 2b is not commutative.

NCERT GUJARATI-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

    Text Solution

    |

  2. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

    Text Solution

    |

  3. If f:R to R is defined by f(x) = x^(2)-3x+2, write f{f(x)}.

    Text Solution

    |

  4. Show that function f: R ->{x in R : -1 < x < 1}defined by f(x)=x/(1+...

    Text Solution

    |

  5. Show that the function f: R->Rgiven by f(x)=x^3is injective.

    Text Solution

    |

  6. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

    Text Solution

    |

  7. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

  8. Given a non-empty set X , consider P\ (X) which is the set of all subj...

    Text Solution

    |

  9. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

    Text Solution

    |

  10. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

    Text Solution

    |

  11. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

    Text Solution

    |

  12. Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...

    Text Solution

    |

  13. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

    Text Solution

    |

  14. Define a binary operation *on the set {0," "1," "2," "3," "4," "5} as ...

    Text Solution

    |

  15. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

    Text Solution

    |

  16. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

    Text Solution

    |

  17. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

    Text Solution

    |

  18. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

    Text Solution

    |

  19. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

    Text Solution

    |