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(6) If A ⊂ R define x+A = {x+a : a ∈ A}. Show that (x+A)∩(x+B)...


(6) If A ⊂ R define x+A = {x+a : a ∈ A}. Show that (x+A)∩(x+B) = x+ (A∩B)
and (x + A) ∪ (x + B) = x + (A ∪ B) when A, B ⊂ R. Moreover, prove that
(x + A)
c = x + Ac and x + (y + A) = (x + y) + A

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