Hi there,
This would give you a deduplicated vector of all possible answers.
# Generate a list of possible answers
PotentialAnswers <- strsplit(Answers, ";") %>%
unlist() %>%
trimws() %>%
unique()
(I added the trimws() because there was a trailing space on one of the answers.)
From there you could you a combination of mutate() and grepl() to generate a TRUE/FALSE for each answer.
As an aside, how is this data coming to you? I'd be anxious with the person and their answers being separate and not keyed together, but that's a separate issue. 
Anyway, I hope that helps!