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

 

[SammyS]

Homework Statement

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

Then your answers are correct.

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

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

Of course you can write them in interval notation as

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

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

.