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Discuss the commutativity and associativ...

Discuss the commutativity and associativity of the binary operation * on R defined by `a*b=a-b+a b` for all `a , b in R ,` where on RHS we have usual addition, subtraction and multiplication of real numbers.

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To determine the commutativity and associativity of the binary operation \( * \) defined on \( \mathbb{R} \) by the expression \( a * b = a - b + ab \), we will proceed step by step. ### Step 1: Check Commutativity To check if the operation is commutative, we need to verify whether \( a * b = b * a \) for all \( a, b \in \mathbb{R} \). 1. **Calculate \( a * b \)**: \[ ...
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Knowledge Check

  • Let Q be the set of all rational numbers and * be the binary operation , defined by a * b=a+ab for all a, b in Q. then ,

    A
    * is commutative but not associative
    B
    *is Associative but not commmutative
    C
    * is neither commutative nor associative
    D
    * is both commutative and associative

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