Final answer:
In data modeling, data associations are represented by dotted arrows that indicate the direction of data flow. Tokens do not flow across data associations. Gateways are not used to show optional data updates.
Step-by-step explanation:
In data modeling, data associations are represented by arrows connecting different elements. The arrowhead of the association depicts the direction of data flow, indicating how data is passed from one element to another. Unlike control flow, where tokens move across control connectors, tokens do not flow across data associations. Therefore, options b and c are not true with respect to data associations.
Thus, the correct answer is option a. Data associations are indeed modeled as dotted arrows. Consequently, option e, which states that both options a and b are true, is not correct.
Gateways, on the other hand, are used to show how process flows can be modified. They do not indicate data updates. Hence, option d is also not true.