If A={x∈R:|x|<2} and B={x∈R:|x-2|≥3}; then

Given A=x∈R,x 3 it implies that -3 3 x 5

If A={x∈R:|x|<2} and B={x∈R:|x-2|≥3}; then

Given A=x∈R,x 3 it implies that -3 3 x 5

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$\begin{array}{l} If A = {x \in R : | x | < 2} and \\ B = {x \in R : | x - 2 | \geq 3}; then \end{array}$

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$A \cap B = (- 2, - 1)$

$A - B = (- 1, 2)$

$B - A = R - (- 2, 5)$

$A \cup B = R - (2, 5)$

answer is D.

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Detailed Solution

$G i v e n A = \{x \in R, |x| < 2\} I t i m p l i e s t h a t - 2 < x < 2$

and

$G i v e n B = \{x \in R, |x - 2| > 3\} i t i m p l i e s t h a t - 3 < x - 2 o r x - 2 > 3 x < - 1 o r x > 5$

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If A={x∈R:|x|<2} and B={x∈R:|x-2|≥3}; then

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$\begin{array}{l} If A = {x \in R : | x | < 2} and \\ B = {x \in R : | x - 2 | \geq 3}; then \end{array}$