JEE Mains · Maths · STD 11 - 1. set theory
Let \(A =\{ x \in R :| x +1|<2\}\) and \(B=\{x \in R:|x-1| \geq 2\}\). Then which one of the following statements is NOT true ?
- A \(A - B =(-1,1)\)
- B \(B - A = R -(-3,1)\)
- C \(A \cap B =(-3,-1]\)
- D \(A \cup B = R -[1,3)\)
Answer & Solution
Correct Answer
(B) \(B - A = R -(-3,1)\)
Step-by-step Solution
Detailed explanation
\(A = \{ x \in R : |x+1| < 2 \} \Rightarrow -2 < x+1 < 2 \Rightarrow -3 < x < 1\) \(A = (-3, 1)\) \(B = \{ x \in R : |x-1| \geq 2 \} \Rightarrow x-1 \geq 2 \text{ or } x-1 \leq -2 \Rightarrow x \geq 3 \text{ or } x \leq -1\) \(B = (-\infty, -1] \cup [3, \infty)\)…
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