Which of the following operations are not distributive?

  • Option 1)

    Standard Multiplication

  • Option 2)

    Standard Addition

  • Option 3)

    a*b=(a.b)^{2};a+b=\left | a \right |\left | b \right |

  • Option 4)

    All are distributive

 

Answers (1)
H Himanshu

As we learnt

 

Distributive Binary operation -

 

a*(b+c)=(a*b)+(a*c)

- wherein

Two binary operation * and + on a set A are functions * : A × A A and +:A x A →A, such that, A × A → A  is said to be distributive, If a*(b+c)=(a*b)+(a*c)

 

 a*(b+c)=a*(\left | b \right |\left | c \right |)

                       =\left (a.(\left | b \right |\left | c \right |) \right )^{2}

                       = a^{2}b^{2}c^{2}

a*b+a*c= \left ( ab \right )^{2}+\left ( ac \right )^{2}= a^{2}b^{2}a^{2}c^{2}= a^{4}b^{2}c^{2}

 

 


Option 1)

Standard Multiplication

Option 2)

Standard Addition

Option 3)

a*b=(a.b)^{2};a+b=\left | a \right |\left | b \right |

Option 4)

All are distributive

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