Final answer:
There is no standard minimum number of hours after which a veteran's service is considered broken upon discharge; the offered options do not apply to the commonly understood definition of 'broken service' in military contexts.
Step-by-step explanation:
The question 'What is the minimum number of hours of service after which a veteran's service is considered broken upon discharge?' does not correspond to a standard or widely recognized criterion for defining a veteran's service as 'broken.' The concept of 'broken service' typically refers to an interruption in a person's military service, not a minimum number of hours served. Therefore, none of the options A) 500 hours B) 750 hours C) 1000 hours D) 1250 hours are applicable under common terminology in military service contexts. If the question reflects specific criteria set forth by an organization or legislation, then it would be important to consult that source directly for the accurate answer.