Prove the following
Question:

If $\mathrm{A}=\{x \in \mathrm{R}:|x|<2\}$ and

$\mathrm{B}=\{x \in \mathrm{R}:|x-2| \geq 3\} ;$ then $:$

 

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

  2. (2) $\mathrm{B}-\mathrm{A}=\mathrm{R}-(-2,5)$

  3. (3) $\mathrm{A} \cup \mathrm{B}=\mathrm{R}-(2,5)$

  4. (4) $\mathrm{A}-\mathrm{B}=[-1,2)$


Correct Option: , 2

Solution:

$A=\{x: x \in(-2,2)\}$

$B=\{x: x \in(-\infty,-1] \cup[5, \infty)\}$

$A \cap B=\{x: x \in(-2,-1]\}$

$A \cup B=\{x: x \in(-\infty, 2) \cup[5, \infty)\}$

$A-B=\{x: x \in(-1,2)\}$

$B-A=\{x: x \in(-\infty,-2] \cup[5, \infty)\}$

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