TRUE/FALSE?
(1) If * is any binary operation on any set S then a * a = a for all a∈S.
(2) If * is any commutative binary operation on any set S, then a*(b*c)=(b*c)*a for all a,b,c∈S.
(3) If * is any associative binary operation on any set S, then a*(b*c)=(b*c)*a for all a,b,c∈S.
(4) The only binary operations of any importance are those defined on sets of numbers.
(5) A binary operation * on a set S is commutative if there exists a,b∈Sa,b∈S such that a*b=b*a.
(6) Every binary operation defined on a set having exactly one element is both commutative and associative.
(7) A binary operation on a set S assigns at least one element of S to each ordered pair of elements of S.
(8) A binary operation on a set S assigns at most one element of S to each ordered pair of elements of S.
(9) A binary operation on a set S assigns at exactly one element of S to each ordered pair of elements of S.
(10) A binary operation on a set S may assign more than one element of S to each ordered pair of elements of S.
