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Valid UML Associations

Brad Perniciaro
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It is my undersanding that a line between two classes (without an arrow) represents a bi-directional association. Is this correct?

Also, is it possible for an association between two classes to be both associative and compositive? In other words, can Class B be both composed of Class A and have a reference to Class A (meaning it would have a UML symbol of both an open arrow and a solid diamond in the same direction)?
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