In UML Use Case diagrams, there are specific relationships that are valid between actors and use cases, as well as between the use cases themselves:
Associationsbetween actors and use cases indicate that an actor participates in the use case. It is depicted as a solid line.
Includesare dependencies that specify that one use case (the base) includes the behavior of another use case (the included). It is depicted with a dashed arrow with the stereotype «include».
Extendsare dependencies where one use case (the extension) conditionally adds to the behavior of another use case (the base). It is depicted with a dashed arrow with the stereotype «extend».
Let's analyze the provided options:
A) This diagram shows simple associations between actors and use cases, which is a valid relationship in UML use case diagrams.
B) This diagram attempts to use include relationships directly between actors and use cases, which is not correct. The «include» relationship is used between use cases, not between an actor and a use case.
C) This diagram shows a solid line arrow from one use case to another, which is not a recognized relationship in UML use case diagrams.
D) This diagram attempts to use extend relationships directly between actors and use cases, which is not correct. The «extend» relationship is used between use cases, not between an actor and a use case.
Therefore, the only diagram that contains only valid relationships according to UML standards is Option A.
[Reference: Object Management Group (OMG) Unified Modeling Language (UML) Specification Version 2.5.1 Section 18.1 on Use Cases, particularly Figure 18.1 which shows the notation for use case diagrams, including actors, use cases, and their relationships., ]
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