Let <math> <mrow> <mi>A</mi> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>∈</mo> <mi>R</mi> <mo>:</mo> <mrow> <mo>|</mo> <mrow> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>|</mo> </mrow> <mo><</mo> <mn>2</mn> </mrow> <mo>}</mo> </mrow> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mtext> </mtext> <mtext> </mtext> <mi>B</mi> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>∈</mo> <mi>R</mi> <mo>:</mo> <mrow> <mo>|</mo> <mrow> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mrow> <mo>|</mo> </mrow> <mo>≥</mo> <mn>2</mn> </mrow> <mo>}</mo> </mrow> <mo>.</mo> </mrow> </math> 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 <math> <mrow> <mi>A</mi> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>∈</mo> <mi>R</mi> <mo>:</mo> <mrow> <mo>|</mo> <mrow> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>|</mo> </mrow> <mo>&lt;</mo> <mn>2</mn> </mrow> <mo>}</mo> </mrow> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mtext> </mtext> <mtext> </mtext> <mi>B</mi> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>∈</mo> <mi>R</mi> <mo>:</mo> <mrow> <mo>|</mo> <mrow> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mrow> <mo>|</mo> </mrow> <mo>≥</mo> <mn>2</mn> </mrow> <mo>}</mo> </mrow> <mo>.</mo> </mrow> </math> Then which one of the following statements is NOT true?

B – A = R – (-3, 1)

Ask & Answer Question

Option 1 -

A – B = (-1, 1)

Option 2 -

B – A = R – (-3, 1)

Option 3 -

$A \cap B = (- 3, - 1]$

Option 4 -

$A \cup B = R - [1, 3)$

3 Views | Posted 2 months ago

Answered by

alok kumar singh | Contributor-Level 10

2 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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