# Short hand interval notation

1. Feb 18, 2012

### rudders93

1. The problem statement, all variables and given/known data
Consider the following intervals:

A = [-3,5), B = (3,8), C = (0,4]

Find: A$\cap$B and A$\cap$C

3. The attempt at a solution

I thought that: A$\cap$B=(3,5) and that A$\cap$C=[0,4] as that is the intersection point, but this book (Schaum's Probability Outlines) says that A$\cap$B=[-3,8) and A$\cap$C=[-3,5)

I'm looking to confirm that the book might be wrong (Amazon reviews indicate alot of typographical errors) and instead maybe their answer refers to $A\cup B$ and $A\cup C$ perhaps? Or am I getting confused?

Thanks!!

2. Feb 18, 2012

### Joffan

The book answers are for union $\cup$, and you are really close to correct with your answers for intersection $\cap$. It could be a typo in either question or answer.

3. Feb 18, 2012

### HallsofIvy

Staff Emeritus
Yes, $A\cap B= (3, 5)$ while $A\cup B= [-3, 8)$ as Joffan says. $A\cup C= [-3, 5)$. But $A\cap C$ is NOT [0, 4] because 0 is not in C.
In fact, C is a subset of A so $A\cap C= C$ and $A\cup C= A$.