Home
Class 12
MATHS
Let ** be a binary operation on NN, the ...

Let `**` be a binary operation on `NN`, the set of natural numbers defined by `a**b=a^(b)` for all `a,binNN` is `**` associative or commutative on `NN`?

A

not commutative

B

associative

C

commutative

D

not associative

Text Solution

Verified by Experts

The correct Answer is:
A,D
Promotional Banner

Topper's Solved these Questions

  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise Integar Answer Type|5 Videos
  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise Matrix Match Type|2 Videos
  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3 (Long Answer Type Questions)|22 Videos
  • ARCHIVE

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|13 Videos
  • BINOMIAL DISTRUTION

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

let ** be a binary operation on ZZ^(+) , the set of positive integers, defined by a**b=a^(b) for all a,binZZ^(+) . Prove that ** is neither commutative nor associative on ZZ^(+) .

If ** be the binary operation on the set ZZ of all integers, defined by a**b=a+3b^(2) , find 2**4.

Let ** be an operation defined on NN , the set of natural numbers, by a**b=L.C.M.(a,b) for all a,binNN . Prove that ** is a binary operation on NN .

let ** be a binary operation on RR , the set of real numbers, defined by a@b=sqrt(a^(2)+b^(2)) for all a,binRR . Prove that the binary operation @ is commutative as well as associative.

Let @ be a binary operation on QQ , the set of rational numbers, defined by a@b=(1)/(8)ab for all a,binQQ . Prove that @ is commutive as well as associative.

(I) Let ** be a binary operation defined by a**b=2a+b-3. Find 3**4. (ii) let ** be a binary operation on RR-{-1} , defined by a**b=(1)/(b+1) for all a,binRR-{-1} Show that ** is neither commutative nor associative. (iii) Let ** be a binary operation on the set QQ of all raional numbers, defined as a**b=(2a-b^(2)) for all a,binQQ . Find 3**5 and 5**3 . Is 3**5=5**3?

Show that an operation ** on RR , the set of real numbers, defined by a**b=3ab+sqrt2, for all a,binRR . Is a binary operaion on RR.

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

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

An operation ** is defined on the set of real numbers RR by a**b=ab+5 for all a,binRR . Is ** a binary operation on RR ?.