Union and Intersection of Sets

[TranscendArcu]

Homework Statement

Let A = {x\in R | |x| >1}, B = {x\in R | -2<x<3}. Find A \cup B and A\cap B

The Attempt at a Solution

I 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, A \cup B = R and A \cap B = { x \in R | -2&lt;x&lt;-1, 1&lt;x&lt;3}. But I'm sure if I have used the correct notation or if these answers are even correct.

 

[SammyS]

Homework Statement

Let A = {x\in R | |x| &gt;1}, B = {x\in R | -2&lt;x&lt;3}. Find A \cup B and A\cap B

The Attempt at a Solution

I 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, A \cup B = R and A \cap B = { x \in R | -2&lt;x&lt;-1, 1&lt;x&lt;3}. But I'm (not?) sure if I have used the correct notation or if these answers are even correct.

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

I take it that you mean:

" Let \text{A}=\{x\in \mathbb{R} | |x| &gt;1\},\ \text{B}=\{x\in \mathbb{R} | -2&lt;x&lt;3\}. Find \text{ A}\cup\text{B} and \text{A}\cap\text{B}\,. "​

Then your answers are correct.

\text{ A}\cup\text{B} = \mathbb{R}

\text{A}\cap\text{B} = \{ x \in \mathbb{R} | -2&lt;x&lt;-1, 1&lt;x&lt;3\}​

Of course you can write them in interval notation as

\text{ A}\cup\text{B} =(-\infty,\,\infty)

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

.