You should answer "Yes."
"Or" in English is usually what is called in logic a non-exclusive "or." That means that "A or B" is considered true if A is true but not B, B is true but not A, or both A and B are true.
Sometimes context or vocabulary will entail that a simple "or" is to be understood as exclusive. For a simple example, the sentence "That was either a zebra or a giraffe" clearly intends an exclusive "or" because nothing is both a zebra and a giraffe. But the general case is that "or" without qualification is non-exclusive. The sentence "The quantitative requirement may be met by taking a year of mathematics or physics" does not mean that taking both math and physics will fail to meet the requirement.
Some people may interpret "either X or Y" as an exclusive "or." Unfortunately that usage is not universal. "Either X or else Y" is one way to specify an exclusive "or." Another is "A or B, but not both."
It is a lexical deficiency in English that it lacks a very sharp division between exclusive "or" (in Latin "aut X aut Y") and non-exclusive (in Latin "vel").