Ben R. answered • 29d

PhD in Mathematics, 9 years college teaching experience

For the first, I would treat the "If x,y ∈ A" part of the statement as "∀ x,y ∈ A" because we want the implication to be true for any x and y we choose from the set A.

For the second, we can interpret that first part of the statement "Given a > 0" as "∀ a > 0", or a bit more formally as "∀ a ∈ R, such that a > 0"