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Show (by giving a step-by-step algebraic derivation from the LHS to the RHS) that if 〈????,∗〉 is a binary algebraic structure where ∗ is commutative, then for all a,b,c ϵ S a*(b*c)= (c*b)*a

Respuesta :

Answer:

Step-by-step explanation:

From the left hand side,

Let b*c = P, and c*b = P'

Then a*(b*c) = a*P

Because * is commutative,

b*c = c*b

a*P = P*a

a*P' = P' *a

are all true

So P = P'

a*P = a*P' (Since P = P')

a*P = P' *a (Since a*P' = P' *a)

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

For all a, b, c in S

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