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

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.

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Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationInequationEasy2 minPYQ_2022

MathematicsEasysingle choice

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?

Options:

Answer:

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.

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Inequation

⏱ 2mℹ️ Source: PYQ_2022

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