How to make brackets larger?

Question

How can the first { and last } in the following be made larger?

  $A =\left \{a \notin\{1, 2\}, \ b\notin \{4,5\}\right\}$.

Answer 1

There are several ways to increase the height of the braces:

1. Use a \vphantom{} inside the \left\{ and \right\} so that the content appears to have greater height causing the size of the braces to increase:

   $B =\left\{ \vphantom{y^2} a \notin \{1, 2\} \right\}$
   

2. Specify a fixed size of the brace (as cmhughes sugested):

   $C =\big\{ \vphantom{y^2} a \notin \{1, 2\} \big\}$
   

3. Or use automatic growth for nested parenthesis as per automatic size adjustment for nested parentheses:

   \setlength\delimitershortfall{-2pt}
   $D =\left\{ a \notin \{1, 2\}  \right\}$
   

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References:

Fixed Size:

• Vertically stretch "/" operator when second (but not first) operand is tall

Automatic Re-size:

• automatic size adjustment for nested parentheses
• "(" or "\left(" parentheses?
• How to adjust brace size for nested braces?

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Code:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
$A =\left\{ \{1, 2\} \right\}$,
$B =\left\{ \vphantom{y^2} \{1, 2\} \right\}$,
$C =\big\{ \{1, 2\} \big\}$,
\setlength\delimitershortfall{-2pt}
$D =\left\{ \{1, 2\}  \right\}$.
\end{document}