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Question

Let A = { x : x ∈ R, |x| < 1}; B = {x : x ∈ R, |x-1| ≥ 1} and

A ∪ B = R - D, then the set D is


A

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B

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C

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D

None of these

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Solution

The correct option is B


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}.


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