Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let * be binary operation defined on R by a * b = 1 + ab, ∀ a, b ∈ R. Then the operation * is (i) commutative but not associative

Let  \ast   be binary operation defined on R by a \ast b = 1 + ab, \forall a, b \in R. Then the operation \ast   is

(i) commutative but not associative

(ii) associative but not commutative

(iii) neither commutative nor associative

(iv) both commutative  and  associative
 

Answers (1)

(i) Here,  

\ast   is a binary operation defined on R by a \ast b = 1 + ab, \forall a, b \in R

So, a \ast b = ab + 1 = b \ast a\\

Therefore,  \ast   is a commutative binary operation.

\\Now, a \ast (b \ast c) = a \ast (1 + bc) = 1 + a (1 + bc) = 1 + a + abc\\ Again, (a \ast b) \ast c = (1 + ab) \ast c = 1 + (1 + ab) c = 1 + c + abc\\ Therefore, a \ast (b \ast c) \neq (a \ast b) \ast c\\

Hence,  \ast  is not associative.

Therefore,  \ast   is commutative but not associative.

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question