Vertical alignment of an array with numbered list

by Subhajit Paul   Last Updated July 12, 2019 11:23 AM - source

please refer to the following scenarios:

Case 1

and

Case 2

The first case is generated by the following part of the script:

\question[5+2]
        Let $ (X,d) $ be a metric space and $ A\subseteq X $. \textit{Boundary} of $ A $ is defined as $ \partial A=\bar{A}\setminus A^{\circ} $. Show that,
        \begin{parts}
%3.a.
            \part[5]
                \[ \begin{array}{rcl}
                \partial A  &=& (A^{\circ}\cup \ext A)^{c}\\[1ex]
                &=& \{x\in X:\forall\d>0, N_{\d}(x)\cap A\ne\emptyset\text{ and }N_{\d}(x)\cap A^{c}\ne\emptyset\}. 
                \end{array} \tag*{\parbox{1pt}{\droppoints}} \]

and the second instance is generated by

\question[5+2]
        Let $ (X,d) $ be a metric space and $ A\subseteq X $. \textit{Boundary} of $ A $ is defined as $ \partial A=\bar{A}\setminus A^{\circ} $. Show that,
        \begin{parts}
%3.a.
            \part[5]
                $\begin{array}{rcl}
                \partial A  &=& (A^{\circ}\cup \ext A)^{c}\\[1ex]
                &=& \{x\in X:\forall\d>0, N_{\d}(x)\cap A\ne\emptyset\text{ and }N_{\d}(x)\cap A^{c}\ne\emptyset\}. 
                \end{array}$\droppoints

What I want is to align the first line of the array with the question number (a). How can I achieve that?

I am using exam class. Here is my preamble.

\documentclass[a5paper,11pt]{exam}
\usepackage[left=0.25in,right=0.75in,top=0.5in,bottom=0.5in,footskip=.15in]{geometry}
\usepackage{amsmath, amssymb, amsthm, amsfonts}
\usepackage[english]{babel}
\usepackage{mathtools}
\usepackage[inline]{enumitem}
\usepackage{mathrsfs}
\usepackage{nccmath}
\usepackage{stmaryrd}
\usepackage{mathdots}
\usepackage{lastpage,refcount}
\footer{}{\small\thepage}{\ifodd\value{page}\relax
    \if\thepage\getpagerefnumber{LastPage}\relax
    \else \tiny {\mbox{\kern\dimexpr+4.75in\relax}}\boxed{\textbf{Turn Over}}
    \fi
    \fi}
\usepackage{etoolbox}
\makeatletter
\setlength\@rightmargin{0.5in}
\patchcmd\[email protected]@toks{\llap{\[email protected]@block}}{\rlap{\[email protected]@block}}{}{}
\patchcmd\droppoints{\llap{\[email protected]@block}}{\rlap{\[email protected]@block}}{}{}
\patchcmd\droptotalpoints{\llap{\[email protected]}}{\rlap{\[email protected]}}{}{}
\patchcmd\droptotalbonuspoints{\llap{\[email protected]}}{\rlap{\[email protected]}}{}{}
\makeatother


\marksnotpoints
\bracketedpoints
\pointsdroppedatright


\renewcommand\partlabel{(\textbf{\alph{partno}})}
\renewcommand{\thesubpart}{(\textit{\roman{subpart}})}
\renewcommand{\subpartlabel}{\thesubpart}
\renewcommand\questionlabel{\textbf{\thequestion.}}

\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\Z}{\mathbb{Z}}
\renewcommand{\a}{\alpha}
\renewcommand{\b}{\beta}
\newcommand{\g}{\gamma}
\renewcommand{\d}{\delta}
\newcommand{\e}{\epsilon}
\DeclareMathOperator{\interior}{int}
\DeclareMathOperator{\ext}{ext}
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}


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