Final answer:
Shawn and Claire, both being Deaf, are most likely to communicate using ASL, which is prevalent in the Deaf community and a core part of Deaf culture.
Step-by-step explanation:
When Shawn and Claire, who are both Deaf, meet for the first time, it is most likely that they will communicate using American Sign Language (ASL). ASL is a complete visual language with its own syntax and grammar, and it is widely used within the Deaf community in the United States. Since Deaf culture values the use of sign language, Shawn and Claire would typically introduce themselves and communicate through signing, which is a natural and primary mode of communication for those who are part of this cultural group.