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(a) Let A ⊂ R be open and B ⊂ R. Define AB = {xy ∈...

(a) Let A ⊂ R be open and B ⊂ R. Define AB = {xy ∈ R : x ∈ A and y ∈ B}. Is AB necessarily open? Why?

(b) Let S = {x ∈ R : x is irrational}. Is S closed? Why?

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