Mark each of the following true or false.
____ a. If * is any binary operation on any set S, then a * a = a for all a ∊ S.
_____ b. If * is any commutative binary operation on any set S, then a * (b * c) = (b *c)*a for all a, b, c ∊ S.
____ c. If* is any associative binary operation on any set 5, then a * (b * c) = (b * c) * a for all a, b, c ∊ S.
____ d. The only binary operations of any importance are those defined on sets of numbers.
_____ e. A binary operation * on a set S is commutative if there exist a,b ∊ S such that a * b = b * a.
_____ f. Every binary operation defined on a set having exactly one element is both commutative and associative.
_____ g. A binary operation on a set S assigns at least one element of S to each ordered pair of elements of S.
_____ h. A binary operation on a set S assigns at most one element of S to each ordered pair of elements of S.
_____ i. A binary operation on a set S assigns exactly one element of S to each ordered pair of elements of S.
______ j. A binary operation on a set S may assign more than one element of S to some ordered pair of elements of S.
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