How to write multiple conditions in separate lines in braced equations?

Question

How do I typeset something like,

 X = 0 if a=1 \& b=1 \& c= 5 \& d=9 ; 
     0 otherwise, 

using those huge left braces and specifying each condition in a line (4 conditions in 4 separate lines)?

Answer 1

It's not clear to me if the conditions for X=1 are separate (logical "or") or cumulative (logical "and"). Assuming it's the former, the following two expressions may meet your needs.

\documentclass{article}
\usepackage{amsmath} % for cases environment and \text command
\begin{document}
\[
X = 
\begin{cases}
  1 & \text{if $a=0$ or $b=1$ or $c=5$ or $d=9$} \\
  0 & \text{otherwise}
\end{cases}
\]

\[
X =
\begin{cases}
1 & \text{if $a=0$} \\
1 & \text{if $b=1$} \\
1 & \text{if $c=5$} \\
1 & \text{if $d=9$} \\
0 & \text{otherwise}
\end{cases}
\]
\end{document} 

Personally, I strongly prefer the first of these two forms -- at least for the setup you've provided. Should the conditions be more elaborate, the second form may well be the better option.

Answer 2

As far as I understand, your want the following construction:

\documentclass{article}
\begin{document}

\[
\left\{
\begin{array}{rl}
X=1 & \mbox{if $a=1$},\\
X=10 & \mbox{if $a=2$},\\
X=100 & \mbox{if $a=3$},\\
X=1000 &\mbox{otherwise}
\end{array}
\right.
\]

or

\[
\left\{
\begin{array}{ll}
X=1 & \mbox{if $a=1$},\\
X=10 & \mbox{if $a=2$},\\
X=100 & \mbox{if $a=3$},\\
X=1000 &\mbox{otherwise}
\end{array}
\right.
\]

\end{document}