Let \( A=\{x: x \in R,|x|1\}, B=\{x: x \in R,|x-1| \geq 1\} \) and ...

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Let \( A=\{x: x \in R,|x|1\}, B=\{x: x \in R,|x-1| \geq 1\} \) and \( A \cup B=R-D \), then set \( D \) is:
(A) \( \quad\{x: 1x \leqslant 2\} \)
(B) \( \quad\{x: 1 \leqslant x2\} \)
(C) \( \quad\{x: 1 \leqslant x \leqslant 2\} \)
(D) None of these
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