# Let A = [x: x $$\in$$ R, |x| < 1]; B = [x : x $$\in$$ R, |x - 1| $$\ge$$ 1] and A $$\cup$$ B = R - D, then the set D is

## Solution :

A = [x: x $$\in$$ R,-1 < x < 1]

B = [x : x $$\in$$ R, x – 1 $$\le$$ -1 or x – 1 $$\ge$$ 1]

[x: x $$\in$$ R, x $$\le$$ 0 or x $$\ge$$ 2]

$$\therefore$$ A $$\cup$$ B = R – D

where D = [x : x $$\in$$ R, 1 $$\le$$ x < 2]

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