Home
Class 12
MATHS
A binary operation * on N defined as a *...

A binary operation * on N defined as `a ** b = a^(3) + b^(3)`, show that * is commutative but not associative.

Text Solution

Verified by Experts

The correct Answer is:
* is commutative but not associative
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise THREE MARKS QUESTIONS WITH ANSWERS|16 Videos
  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise SIX MARKS QUESTIONS WITH ANSWERS|7 Videos
  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TRY YOURSELF - EXERCISE (Five marks questions)|1 Videos
  • PUC SUPPLEMENTARY EXAMINATION QUESTION PAPER JUNE 2019

    SUBHASH PUBLICATION|Exercise PART E|4 Videos
  • SUPER MODEL QUESTION PAPER FOR PRACTICE

    SUBHASH PUBLICATION|Exercise PART - E|4 Videos

Similar Questions

Explore conceptually related problems

A binary operation * on N defined as a ** b = sqrt(a^(2) + b^(2)) , show that * is both cummutative and associative.

Let * be a binary operation on the set R defined by a ** b = (a + b)/2 . Show that * is commulative but not associative.

Let * be a binary operation on N defined by a ** b = HCF of a and b. Show that * is both commutative and associative.

Let A = N xx N 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.

Binary operation * on R -{-1} defined by a ** b = (a)/(b+1) is

On Q, define * by a ** b = (ab)/4 . Show that * is both commutative and associative.

Binary operation * on R - {-1} defined by a * b= (a)/(b+a)

On Q, define * by a ** b = (2ab)/3 . Show that * is both cummutative and associative.

Let * be a Binary operation defined on N by a ** b = 2^(ab) . Prove that * is commutative.

Consider the binary opertions **: R xx R to R and o : R xx R to 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 AA a,b,c in R, a ** (b o c) = (a**b) o (a **c). [If it is so, we say that the opertion ** distributes over the opertion 0]. Does o distribute over ** ? Justify your answer.