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<2 ⇒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.

Q31 / 90 · JEE Main 2022 (25 Jun Shift 2) · Mathematics

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

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

Solution

Given,

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

$\Rightarrow A = (- 3, 1)$

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

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

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

$\Rightarrow B - A = R - (- 3, 3)$

So, option $B$ is not true.

Hence, the correct answer is option: 'B'.

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

Solution

Relevant Questions

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