If A - x - R - x -2 and B - x - R - x -2- - 3- thenA- A - B -2-1B- A-B-1-2- B - A - R -2-5D- A - B - R -2-5

The correct option is C B A=ℝ ( 2,5)A={x∈ℝ:|x| lt;2} ⇒ A={ x: x∈( 2,2)} nbsp; and B={ x∈ℝ: |x 2|≥ 3} ⇒ x 2 ≥ 3 or x 2≤ 3 ⇒ x ≥ 5 or x≤ 1 nbsp;⇒ B={ ...

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Byju's Answer

Standard XII

Mathematics

Difference of Two Sets

If A = x ∈ R ...

Question

If $A = {x \in R : | x | < 2}$ and $B = {x \in R : | x - 2 | \geq 3},$ then

A \cap B = (- 2, - 1)

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B - A = R - (- 2, 5)

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A - B = [- 1, 2)

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A \cup B = R - (2, 5)

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Solution

The correct option is B $B - A = R - (- 2, 5)$
$A = {x \in R : | x | < 2}$
$\Rightarrow A = {x : x \in (- 2, 2)}$

and $B = {x \in R : | x - 2 | \geq 3}$
$\Rightarrow x - 2 \geq 3 or x - 2 \leq - 3$
$\Rightarrow x \geq 5 or x \leq - 1$
$\Rightarrow B = {x : x \in (- \infty, - 1] \cup [5, \infty)}$

Now, $A \cap B = (- 2, - 1]$
$A \cup B = (- \infty, 2) \cup [5, \infty)$
$A - B = (- 1, 2)$
$B - A = (- \infty, - 2] \cup [5, \infty)$

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If A={x∈R:|x|<2} and B={x∈R:|x−2|≥3}, then

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