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If A = {x ∈ R : |x + 1| < 2} and B = {x ∈ R : |x - 1| >= 2}, then (B - A) is equal to (where R is set…

- \(A = \{x \in \mathbb{R} : |x + 1| < 2\} = (-3, 1)\). - \(B = \{x \in \mathbb{R} : |x - 1| \ge 2\} = (-\infty, -1] \cup [3, \infty)\). Therefore, \(B - A = ((-\infty, -1]…

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If A = {x ∈ R : |x + 1| < 2} and B = {x ∈ R : |x - 1| >= 2}, then (B - A) is equal to (where R is set of real numbers)

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Correct answer B

- A={x∈R:∣x+1∣<2}=(−3,1)A = \{x \in \mathbb{R} : |x + 1| < 2\} = (-3, 1).
- B={x∈R:∣x−1∣≥2}=(−∞,−1]∪[3,∞)B = \{x \in \mathbb{R} : |x - 1| \ge 2\} = (-\infty, -1] \cup [3, \infty).
Therefore, B−A=((−∞,−1]∪[3,∞))∖(−3,1)=(−∞,−3]∪[3,∞)=R−(−3,3)B - A = ((-\infty, -1] \cup [3, \infty)) \setminus (-3, 1) = (-\infty, -3] \cup [3, \infty) = \mathbb{R} - (-3, 3).

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