Home
Class 12
MATHS
The binary operation * define on N by a*...

The binary operation * define on N by a*b = a+b+ab for all `a,binN` is

A

commutative only

B

associative only

C

commutative and associative both

D

none of these

Text Solution

Verified by Experts

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Prove that the binary operation @ defined on QQ by a@b=a-b+ab for all a,b in QQ is neither commutative nor associative.

Prove that the binary operation ** on RR defined by a**b=a+b+ab for all a,binRR is commutative and associative.

Knowledge Check

  • The binary operation ** defined on NN by a**b=a+b+ab for all a,binNN is--

    A
    commutaitive only
    B
    associative only
    C
    commutative and associative both
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    On the set Q^+ of all positive rational numbers if the binary operation * is defined by a * b = 1/4ab for all a,b in Q^+ find the identity element in Q^+ .

    Discuss the commutativity and associativity of binary operation ** defined on ZZ by the rule a**b=|a|b for all a,binZZ .

    Find the identity element of the binary operation ** on ZZ defined by a**b=a+b+1 for all a,binZZ .

    A binary operation @ is defined on RR-{-1} by a@b=a+b+ab for all a,binRR-{-1}. (i) Discuss the commutativity and associativity of @ on RR-{-1} . Find the identity element, if exists. (iii) Prove that every element of RR-{-1} is invertible.

    Let S be any set containing more than two elements. A binary operation @ is defined on S by a@b=b for all a,binS . Discuss the commutativity and associativity of @ on S.

    Show that identity of the binary operation ** on RR defined by a**b=|a+b| for all a,binRR, does not exist.

    Let A={0,1,2,3,4,5} be a given set, a binary operation @ is defined on A by a@b=ab(mod6) for all a,bin A. Find the identity element for @ in A . Show that 1 and 5 are the only invetible elements in A.

    Home
    Profile