Home
Class 12
MATHS
Let ** be the binary opertion on N defin...

Let `**` be the binary opertion on N defined by `a **b=H.C.F.` of a and b. Is `**` commutative ? Is `**` associative ? Does there exist identity for this binary opertion on N ?

Text Solution

Verified by Experts

The correct Answer is:
`**` is both commutative and associative;` **` does not have any identity in N
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT TELUGU|Exercise MISCLELLANEOUS EXERCISE ON CHAPTER 1|18 Videos

  • RELATIONS AND FUNCTIONS

    NCERT TELUGU|Exercise EXERCISE 1.3|14 Videos

  • PROBABILITY

    NCERT TELUGU|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos

  • VECTOR ALGEBRA

    NCERT TELUGU|Exercise Miscellaneous Exercise on chapter 10|17 Videos

Similar Questions

Explore conceptually related problems

If a * b = H.C.F. of a and b on N. Verify binary opertion commutative, associative. Does there exists identity element.

Show that *: R xx R to R defined by a*b = 3a + 5b is non commutative and non associative:

Let A = N x N and (a,b)*(c,d) = (a+c, b+d) on A. Show that * is commutative and associative. Find the identity element if exists.