Let A = \ x ∈ R: |x + 1| < 2\ and B = \ x ∈ R: |x - 1| ≥ 2\ . Then which one the following statements is NOT true?

Correct answer: B. B - A = R - (- 3, 1) Given, A = \ x ∈ R: |x + 1| ⇒ A = (- 3, 1) Now, B = \ x ∈ R: |x - 1| ≥ 2\ ⇒ B = ( - ∞ , - 1 ] [ 3, ∞ ) Now, B - A = ( - ∞ , - 3 ] [ 3, ∞ ) ⇒ B - A = R - (- 3, 3) So, option B is not true.

JEE Main 202225 JuneEvening Shift

Exam: JEE Main
Year: 2022
Date: 25 June
Shift: Evening Shift
Subject: Mathematics
Chapter: Basics of Mathematics

JEE Main 2022 · 25 June · Evening Shift · Mathematics · Basics of Mathematics

Let A = \ x ∈ R: |x + 1| < 2\ and B = \ x ∈ R: |x - 1| ≥ 2\ . Then...

Let

A = \left\{x \in R: \left|x + 1\right| < 2\right\}

and

B = \left\{x \in R: \left|x - 1\right| \ge 2\right\}

. Then which one the following statements is NOT true?

Options

A $A - B = \left(- 1, 1\right)$
B $B - A = R - \left(- 3, 1\right)$
C $A \cap B = ( - 3, - 1 ]$
D $A \cup B = R - [ 1, 3 )$

Correct answer

B. $B - A = R - \left(- 3, 1\right)$

Step-by-step solution

Given,

$A = \left\{x \in R: \left|x + 1\right| < 2\right\}$

$⇒ A = \left(- 3, 1\right)$

Now, $B = \left\{x \in R: \left|x - 1\right| \ge 2\right\}$

$⇒ B = ( - \infty , - 1 ] \cup [ 3, \infty )$

Now, $B - A = ( - \infty , - 3 ] \cup [ 3, \infty )$

$⇒ B - A = R - \left(- 3, 3\right)$

So, option $B$ is not true.

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