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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Let * be binary operation defined on R by $ a*b=1+ab, a,b \in R.$ Then the operation * is

(i) commutative but not associative (ii) associative but not commutative (iii) neither commutative nor associative (iv) both commutative and associative
Can you answer this question?
 
 

1 Answer

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Toolbox:
  • 1. A binary operation * defined on R is commutative if $a*b=b*a$
  • 2. A binary operation * defined on R is associative if $(a*b)*c=a*(b*c) \qquad a,b \in R$
Step 1: commutative
 
* operation defined on R by
 
$a*b=1+ab \qquad a,b \in R$
 
$b*a=1+ba$
 
$=1+ab$
 
Multiplication is commutative in R
 
$ a*b =b*a$
 
* operation is commutative
 
Step 2: Associative
 
$(a*b)*c=(1+ab)*c$
 
$=1+(1+ab)c$
 
$=1+c+abc$
 
$a \times (b \times c)=a * (1+bc)$
 
$=1+a(1+bc)$
 
$=1+a+abc$
 
$(a*b)*c \neq a *(b*c)$
 
* operation is not associative
 
Solution: * operation is commutative but not associative
 
(i) option is correct

 

 

answered Mar 5, 2013 by meena.p
edited Mar 27, 2013 by meena.p
 

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