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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