Let A = {x : x ∈ R, |x| < 1}, B = {x : x ∈ R, |x – 1| ≥ 1} and A ∪ B = R – D, then set D is:

{x : 1 < x ≤ 2} {x : 1 ≤ x < 2} {x : 1 ≤ x ≤ 2} None of these

{x : 1 ≤ x < 2}

We have A = {x : x ∈ R, –1 < x < 1}, B = {x : x ∈ R, x – 1 ≤ –1 or x – 1 ≥ 1} = {x : x ∈ R, x ≤ 0 or x ≥ 2} ∴ A ∪ B = R – D Where D = {x : x ∈ R, 1 ≤ x < 2} Hence (2) is the correct answer.