Let A = { x ∈ R : | x + 1 | < 2 } a n d B { x ∈ R : | x − 1 | ≥ 2 } . Then which one of the following statements is NOT true?

Kindly go through the solution − 2 < x + 1 < 2 − 3 < x < 1 | x − 1 ≤ − 2 o r x − 1 ≥ 2 x ≤ − 1 o r x ≥ 3

Let $A = {x \in R : | x + 1 | < 2} a n d B {x \in R : | x - 1 | \geq 2} .$ Then which one of the following statements is NOT true?

Option 1 - A – B = (-1, 1)

Option 2 - B – A = R – (-3, 1)

Option 3 - <math> <mrow> <mi>A</mi> <mo>∩</mo> <mi>B</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>3</mn> <mo>,</mo> <mo>−</mo> <mrow> <mrow> <mn>1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </mrow> </mrow> </math>

Option 4 - <math> <mrow> <mi>A</mi> <mo>∪</mo> <mi>B</mi> <mo>=</mo> <mi>R</mi> <mo>−</mo> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>,</mo> <mrow> <mrow> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </mrow> </math>

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Answered by

Alok Kumar Singh | Contributor-Level 10

8 months ago

Correct Option - 2

Detailed Solution:

Kindly go through the solution

$\begin{array}{l} - 2 < x + 1 < 2 \\ - 3 < x < 1 \end{array} | \begin{matrix} x - 1 \leq - 2 o r x - 1 \geq 2 & x \leq - 1 o r x \geq 3 \end{matrix}$

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