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Assume that is a binary operation on a non empty set A, and suppose that is both commutative and associative. Use the definitions of the commutative and associative properties to show that [ (ab)c ]d=(dc)(ab) for all a,b,c and d in A.

In each part following, a rule that determines a binary operation on the set of all integers is given. Determine in each case whether the operation is commutative or associative and whether there is an identity element. Also find the inverse of each invertible element. b. d. f. h. j. l. for n. for

Suppose that you start browsing the internet on a specified page c. Let x be all the websites you can reach by following links, starting at x. Give a reccursive defintion for the set x including both the recursive part and the base case.