   Chapter 1.4, Problem 13E

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# Assume that ∗ is an associative binary operation on the non empty set A . Prove that a ∗ [ b ∗ ( c ∗ d ) ] = [ a ∗ ( b ∗ c ) ] ∗ d for all a , b , c , and d in A .

To determine

To prove: a[b(cd)]=[a(bc)]d for all a,b,c, and d in A, where is an associative binary operation on the non empty set A.

Explanation

Given Information:

Associative binary operation on the non empty set A is *.

Formula Used:

If is an associative binary operation on the non empty set A then for all x,y,zA, we have, x(yz)=(xy)z.

Explanation:

Consider the left side of a[b(cd)]=[a(bc)]d,

a[b(cd)]</

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