A={x:x∈R,|x|<1}, B={x:x∈R,|x−1|≥1} and A∪B=R−D then D =

|x|<1⇒−1<x<1; |x−1|≥1⇒x−1≤−1 or x−1≥1⇒x≤0 or x≥2A∪B={x:−1<x<1 or x≤0 or x≥2} ={x:x<1 or x≥2}∴D=R−(A∪B)={x:1≤x<2}

A={x:x∈R,|x|<1}, B={x:x∈R,|x−1|≥1} and A∪B=R−D then D =

|x|<1⇒−1<x<1; |x−1|≥1⇒x−1≤−1 or x−1≥1⇒x≤0 or x≥2A∪B={x:−1<x<1 or x≤0 or x≥2} ={x:x<1 or x≥2}∴D=R−(A∪B)={x:1≤x<2}

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$A = {x : x \in R, | x | < 1}, B = {x : x \in R, | x - 1 | \geq 1}$ and $A \cup B = R - D$ then D =

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${x : 1 \leq x < 2}$

${x : 1 \leq x \leq 2}$

Empty set

${x : 1 < x \leq 2}$

answer is B.

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$| x | < 1 \Rightarrow - 1 < x < 1; | x - 1 | \geq 1 \Rightarrow x - 1 \leq - 1 o r x - 1 \geq 1 \Rightarrow x \leq 0 o r x \geq 2$

$\begin{array}{rcl} A \cup B & = & {x : - 1 < x < 1 o r x \leq 0 o r x \geq 2} \\ = & {x : x < 1 o r x \geq 2} \end{array}$

$∴ D = R - (A \cup B) = {x : 1 \leq x < 2}$

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A={x:x∈R,|x|<1}, B={x:x∈R,|x−1|≥1} and A∪B=R−D then D =

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$A = {x : x \in R, | x | < 1}, B = {x : x \in R, | x - 1 | \geq 1}$ and $A \cup B = R - D$ then D =