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修改阵列环境困难

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修改阵列环境困难

我有一个数组，之前曾得到过帮助，现在我正尝试修改该数组。但是，在这样做时，我的“定理”的某些部分不断移到下一行。

以下是 MWE：

\documentclass{article}
\usepackage{amsmath,array}% http://ctan.org/pkg/{amsmath,array}
\newcommand{\twolinebrace}{\rlap{$\smash{\raisebox{.5\height}{\bigg\}}}$}}
\newlength{\LHS}\newlength{\RHS}
\newcolumntype{M}{>{$}p{\LHS}<{$}}
\newcolumntype{N}{>{$}p{\RHS}<{$}}
\begin{document}
\begin{theorem}
Let $\{A_{\alpha \colon \alpha \in A}\}$ and $\{B_{\beta \colon \beta \in  B}\}$ be families of subsets if a set $X$. Then:
\[
\renewcommand{\arraystretch}{1.1}
\begin{array}{@{}l@{\quad}l@{}}
\left.\kern-\nulldelimiterspace\\
             \begin{array}                                                                       {>{\bfseries}p{2em}@{\quad}M@{\quad$=$\quad}N}
  (a) & \big(\bigcup_{\alpha\in A} A_{\alpha}\big) \cup \big(\bigcup_{\beta\in B} B_{\beta}\big) & \bigcup_{(\alpha,\beta)} A_{\alpha} \cup B_{\beta}\\
  (b) & \bigg(\bigcap_{\alpha \in A A_{\alpha}} \bigg) \cap \bigg(\bigcap_{\beta \in B B_{\beta}} \bigg) &  \bigcap_{(\alpha,\beta)} A_{\alpha} \cap B_{\beta} 
\end{array}\right\} & {\text{Associative Laws}} \\
\left.\kern-\nulldelimiterspace\begin{array}{>{\bfseries}p{2em}@{\quad}M@{\quad$=$\quad}N}
  (c) & X \cup (Y \cup Z) & (X \cup Y) \cup Z \\
  (d) & X \cap (Y \cap Z) & (X \cap Y) \cap Z 
\end{array}\right\} & {\text{Associative Laws}} \\
\left.\kern-\nulldelimiterspace\begin{array}{>{\bfseries}p{2em}@{\quad}M@{\quad$=$\quad}N}
  (e) & X \cup (Y \cap Z) & (X \cup Y) \cap (X \cup Z) \\
  (f) & X \cap (Y \cup Z) & (X \cap Y) \cup (X \cap Z)
\end{array}\right\} & {\text{Distributive Laws}} \\
\end{array}
\]
\end{theorem}
\end{document}

我需要添加到我的数组中，但现在我遇到了更多问题。现在，“文本”‘结合律’、‘分配律’和‘德摩根定律’无法正确显示。这是我最新的 MWE：

\documentclass{article}
\usepackage{amsmath,array}% http://ctan.org/pkg/{amsmath,array}
\newcommand{\twolinebrace}{\rlap{$\smash{\raisebox{.5\height}{\bigg\}}}$}}
\newlength{\LHS}\newlength{\RHS}
\newcolumntype{M}{>{$}p{\LHS}<{$}}
\newcolumntype{N}{>{$}p{\RHS}<{$}}
\begin{document}
\begin{theorem}
Let $\{A_{\alpha \colon \alpha \in A}\}$ and $\{B_{\beta \colon \beta \in  B}\}$ be families of subsets of a set~$X$. Then:
\[
\renewcommand{\arraystretch}{1.25}
\begin{array}{@{}l@{\quad}l@{}}
\left.\kern-\nulldelimiterspace\begin{array}{>{\bfseries}p{2em}@{\quad}M@{\quad$=$\quad}N}
(a) & X \cup Y &  Y \cup X \\
  (b) & X \cap Y &  X \cap Y
\end{array}\right\} & {\text{Commutative Laws}} \\
\left.\kern-\nulldelimiterspace\begin{array}{>{\bfseries}p{2em}@{\quad}M@{\quad$=$\quad}N}
(c) & X \cup (Y \cup Z) & (X \cup Y) \cup Z \\
  (d) & X \cap (Y \cap Z) & (X \cap Y) \cap Z 
\end{array}\right\} & {\text{Associative Laws}} \\
\left.\kern-\nulldelimiterspace\begin{array}{>{\bfseries}p{2em}@{\quad}M@{\quad$=$\quad}N}
(e) & X \cup (Y \cap Z) & (X \cup Y) \cap (X \cup Z) \\
  (f) & X \cap (Y \cup Z) & (X \cap Y) \cup (X \cap Z)
\end{array}\right\} & {\text{Distributive Laws}} \\
\end{array}
\]
\end{theorem}

对于此事，我们将非常感激任何额外的帮助。

答案1

也许下面的描述更加清晰一些：

在此处输入图片描述

\documentclass{article}
\usepackage{amsmath,amsthm,array}% http://ctan.org/pkg/{amsmath,amsthm,array}
\newcommand{\twolinebrace}{\left.\kern-\nulldelimiterspace\begin{array}{@{}c@{}}\\\\\end{array}\right\}}
\newtheorem{theorem}{Theorem}
\begin{document}
\begin{theorem}
Let $\{A_{\alpha \colon \alpha \in A}\}$ and $\{B_{\beta \colon \beta \in  B}\}$ be families of subsets if a set~$X$. Then:
\[
  \renewcommand{\arraystretch}{1.25}
  \begin{array}{@{}l@{\quad}l@{}}
    \begin{array}{>{\bfseries}p{2em}@{\quad}r@{{}={}}l}
      (a) & 
        \big(\bigcup_{\alpha\in A} A_{\alpha}\big) \cup \big(\bigcup_{\beta\in B} B_{\beta}\big) & % LHS
        \bigcup_{(\alpha,\beta)} A_{\alpha} \cup B_{\beta} \\ % RHS
      (b) & 
        \big(\bigcap_{\alpha \in A} A_{\alpha} \big) \cap \big(\bigcap_{\beta \in B} B_{\beta} \big) & % LHS
        \bigcap_{(\alpha,\beta)} A_{\alpha} \cap B_{\beta} % RHS
    \end{array} & \twolinebrace\text{Associative Laws} \\
    \begin{array}{>{\bfseries}p{2em}@{\quad}r@{{}={}}l}
      (c) & 
        X \cup (Y \cup Z) & % LHS
        (X \cup Y) \cup Z \\ % RHS
      (d) & 
        X \cap (Y \cap Z) & % LHS
        (X \cap Y) \cap Z % RHS
    \end{array} & \twolinebrace\text{Associative Laws} \\
    \begin{array}{>{\bfseries}p{2em}@{\quad}r@{{}={}}l}
      (e) & 
        X \cup (Y \cap Z) & % LHS
        (X \cup Y) \cap (X \cup Z) \\ % RHS
      (f) & 
        X \cap (Y \cup Z) & % LHS
        (X \cap Y) \cup (X \cap Z) % RHS
    \end{array} & \twolinebrace\text{Distributive Laws}
  \end{array}
\]
\end{theorem}
\end{document}

请注意，使用array类似这样的（或者只是在显示中设置内容\[... \]）它不能跨页面边界中断。如果您希望克服此限制，则必须将显示设置为列表，或者将其拆分为包含每个“规则对”的单独块，允许内容在中间中断。

答案2

与上面的不同，但我不建议多次使用。原因是每次你都必须调整标签。但无论如何，这里是：

\documentclass{article}
\usepackage{amsmath,amsthm}% http://ctan.org/pkg/{amsmath,array}
\usepackage{picture}
\usepackage{enumitem}
\newtheorem{theorem}{Theorem}
\begin{document}
\begin{theorem}
Let $\{A_{\alpha \colon \alpha \in A}\}$ and $\{B_{\beta \colon \beta \in  B}\}$ be families of subsets if a set $X$. Then:
\begin{enumerate}[label=\bfseries(\alph*)]
    \item $\big(\bigcup_{\alpha\in A} A_{\alpha}\big) \cup \big(\bigcup_{\beta\in B} B_{\beta}\big) = \bigcup_{(\alpha,\beta)} A_{\alpha} \cup B_{\beta}$
    \item $\big(\bigcap_{\alpha \in A} A_{\alpha} \big) \cap \big(\bigcap_{\beta \in B} B_{\beta} \big)=\bigcap_{(\alpha,\beta)} A_{\alpha} \cap B_{\beta}$
                \makebox(0,0){\put(0,10ex){%
               $\left.\rule{0pt}{5ex}\right\}$ Associative Laws}}
    \item $X \cup (Y \cup Z)= (X \cup Y) \cup Z$  
  \item $X \cap (Y \cap Z) = (X \cap Y) \cap Z$
                \makebox(0,0){\put(7em,10ex){%
               $\left.\rule{0pt}{5ex}\right\}$ Associative Laws}}
  \item $X \cup (Y \cap Z) = (X \cup Y) \cap (X \cup Z)$
  \item $X \cap (Y \cup Z) = (X \cap Y) \cup (X \cap Z)$
                \makebox(0,0){\put(4.25em,10ex){%
               $\left.\rule{0pt}{5ex}\right\}$ Distributive Laws}}
\end{enumerate}
\end{theorem}
\end{document}

在此处输入图片描述

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