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Which of the following binary operations are not commutative?

  • Option 1)

    a*b=a+b

  • Option 2)

    a*b=ab

  • Option 3)

    a*b*c=a+b+c

  • Option 4)

    a*b*c=ab+c

 

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As we learnt

 

Commutative Binary operation -

 

a * b = b * a  

- wherein

A binary operation * on a set A is a function * : A × A → A. It is called commutative, if a * b = b * a, for every a, b ∈ A.
 

 

 ab+c\neq ac+b\neq bc+a

This operator is not commutative.

 


Option 1)

a*b=a+b

Option 2)

a*b=ab

Option 3)

a*b*c=a+b+c

Option 4)

a*b*c=ab+c

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Himanshu

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