If A-x-x-2 and B- x- -x-2- 3- then

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={ x: x∈ ( ∞, 1]∪ [5,∞)} Now, A∩ B=( 2, ...

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Byju's Answer

Standard XII

Mathematics

Difference of Two Sets

If A=x∈ℝ:|x|<...

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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Similar questions

If the sets $A$ and $B$ are defined as

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f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 2 sin (- \frac{π x}{2}), & if x < - 1 | a x^{2} + x + b |, & if - 1 \leq x \leq 1 sin (π x) & if x > 1 \end{matrix}

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

The correct option is B B−A=R−(−2,5)A={x∈R:|x|<2} ⇒A={x:x∈(−2,2)} and B={x∈R:|x−2|≥3} ⇒x−2≥3 or x−2≤−3 ⇒x≥5 or x≤−1 ⇒B={x:x∈(−∞,−1]∪[5,∞)} Now, A∩B=(−2,−1] A∪B=(−∞,2)∪[5,∞) A−B=(−1,2) B−A=(−∞,−2]∪[5,∞)

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