Let A = {x : x ∈ R, |x| < 1}, B = {x : x ∈ R, |x – 1| ≥ 1} and A ∪ B = R – D, then set D is:
Answer & explanation
Correct answer: option 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.