Discuss the commutativity and associativity of the binary operation * on R defined by `a*b=(a b)/4 ` for `a l la ,b in Rdot`

Explanation

`a{ }^{*} b=a-b+a b forall a, b in A=Q-{1}`

`
b^{*} a=b-a+b a`

`
(a^{*} b) ne b^{*} a therefore *` not commutative.

`
(a^{*}b) ^{*} c=(a-b+a b)^{*} c`

`
=a-b-c+a b+a c-b c+a b c`

`
a(b^{*} c) =a *(b-c+b c) =a-b+c+a b-a c-b c+a b c `

`
(a * b)^{*} c ne a^{*}(b^{*} c) `

`
therefore *` is not associative.