In: Advanced Math
(a) Let Λ = {λ ∈ R : 0 < λ < 1}. For each λ ∈ Λ, let Aλ = {x ∈ R : −λ < x < 1/λ}. Find U λ∈Λ Aλ and ~U λ∈Λ Aλ respectively.
(b) Let Λ = \ {λ ∈ R : λ > 1}. For each λ ∈ Λ, let Aλ = {x ∈ R : −λ < x < 1/λ}. Find U λ∈Λ Aλ and ~U λ∈Λ Aλ respectively.
please note that the results have been done with rigour. With you merely seek the final answer, Please find them in the answer.