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Union and Intersection of Sets

  1. Jan 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Let [itex]A = {x\in R | |x| >1}, B = {x\in R | -2<x<3}[/itex]. Find A \cup B and A\cap B

    3. The attempt at a solutionI thought I might attempt this via a number line. Since I don't know how to make a number line in Latex, I'll describe it. I have A as being all of R except for the region bounded from -1 < x < 1. I have B as the region bounded from -2<x<3.

    I then observed, [itex]A \cup B = R[/itex] and [itex]A \cap B = { x \in R | -2<x<-1, 1<x<3} [/itex]. But I'm sure if I have used the correct notation or if these answers are even correct.
     
  2. jcsd
  3. Jan 6, 2012 #2

    SammyS

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    To make the braces, { , } , show in LaTeX, use the backslash, \ , character with each brace: \{ , \} .

    I take it that you mean:
    " Let [itex]\text{A}=\{x\in \mathbb{R} | |x| >1\},\ \text{B}=\{x\in \mathbb{R} | -2<x<3\}[/itex]. Find [itex]\text{ A}\cup\text{B}[/itex] and [itex]\text{A}\cap\text{B}\,.[/itex] "

    Then your answers are correct.
    [itex]\text{ A}\cup\text{B} = \mathbb{R}[/itex]

    [itex]\text{A}\cap\text{B} = \{ x \in \mathbb{R} | -2<x<-1, 1<x<3\} [/itex]​

    Of course you can write them in interval notation as
    [itex]\text{ A}\cup\text{B} =(-\infty,\,\infty)[/itex]

    [itex]\text{A}\cap\text{B} =(-2,\,-1)\cup(1,\,3)[/itex]​

    .
     
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