Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let ∗ be the binary operation on N defined by a ∗ b = H.C.F. of a and b. Is ∗ commutative? Is ∗ associative? Does there exist identity for this binary operation on N?

Q. 8 Let ∗ be the binary operation on N defined by a ∗ b = H.C.F. of a and b.
Is ∗ commutative? Is ∗ associative? Does there exist identity for this binary
operation on N?

Answers (1)

best_answer

a ∗ b = H.C.F. of a and b for all a,b \in A

H.C.F. of a and b = H.C.F of b and a for all a,b \in A

\therefore \, \, \, \, a*b=b*a

Hence, operation  ∗  is commutative.

For  a,b,c \in N ,

(a*b)*c = (H.C.F \, of\, a\, and\, b)*c= H.C.F\, of \, a,b,c.

  a*(b*c )= a*(H.C.F \, of\, b\, and\, c)= H.C.F\, of \, a,b,c.

\therefore                (a*b)*c=a*(b*c) 

Hence,  ∗ is associative.

An element c \in N will be identity for operation *  if a*c=a= c*a  for a \in N.

Hence, the operation * does not have any identity in N.

 

 

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

No changes in exam, IA system: CBSE rebuts claims of syllabus reduction, open book exams in 2025
anam-khan

Fact-check: CBSE hasn't reduced syllabus by 15%, internal assessments will not be 40% of score in 2025
anam-khan

CBSE date sheet 2025 for Classes 10, 12 likely in November last week: Reports

Latest Question