How to draw this image in LaTeX?

Question

I would like to be able to draw this image in LaTeX but have no idea how to do so. I am new to graphs in LaTeX so any help would be much appreciated.

The red, green and blue circles along with annotations are not part of the image; they are there to explain length requirements. Also, the final graph produced need not follow that same format. As long as all the lines are drawn, I would be able to work out the positioning.

It is also a proper subset symbol, not a C. Thank you in advance.

Edit: I figured it out after the suggestion to use Tikz (thank you @SebGlav).

\begin{center}
\begin{tikzpicture}[scale=1.5]

\node (a) at (0,0) [fill,circle,inner sep=1.2pt] {};
\node (b) at (1,0) [fill,circle,inner sep=1.2pt] {};
\node (c) at (4,0) [fill,circle,inner sep=1.2pt] {};
\node (d) at (5,0) [fill,circle,inner sep=1.2pt] {};
\draw (0,0) -- (1,0) -- (4,0) -- (5,0);
\draw [gray,decorate,decoration={brace,amplitude=5pt},
       xshift=0pt,yshift=-4pt]
   (1,0) -- (0,0) 
   node [black,midway,below=4pt,xshift=0pt]
   {\footnotesize $I_1$};
\draw [gray,decorate,decoration={brace,amplitude=5pt},
       xshift=0pt,yshift=-4pt]
   (4,0) -- (1,0) 
   node [black,midway,below=4pt,xshift=0pt]
   {\footnotesize $I_2$};
\draw [gray,decorate,decoration={brace,amplitude=5pt},
       xshift=0pt,yshift=-4pt]
   (5,0) -- (4,0) 
   node [black,midway,below=4pt,xshift=0pt]
   {\footnotesize $I_3$};
   
\end{tikzpicture}

\bigskip

\begin{tikzpicture}[scale=1.5]
   
\node (a) at (0,0) [fill,circle,inner sep=1.2pt] {};
\node (b) at (2,0) [fill,circle,inner sep=1.2pt] {};
\node (c) at (3,0) [fill,circle,inner sep=1.2pt] {};
\node (d) at (5,0) [fill,circle,inner sep=1.2pt] {};
\draw (0,0) -- (1,0) -- (4,0) -- (5,0);
\draw [gray,decorate,decoration={brace,amplitude=5pt},
       xshift=0pt,yshift=-4pt]
   (2,0) -- (0,0) 
   node [black,midway,below=4pt,xshift=0pt]
   {\footnotesize $I'_1$};
\draw [gray,decorate,decoration={brace,amplitude=5pt},
       xshift=0pt,yshift=-4pt]
   (3,0) -- (2,0) 
   node [black,midway,below=4pt,xshift=0pt]
   {\footnotesize $I'_2$};
\draw [gray,decorate,decoration={brace,amplitude=5pt},
       xshift=0pt,yshift=-4pt]
   (5,0) -- (3,0) 
   node [black,midway,below=4pt,xshift=0pt]
   {\footnotesize $I'_3$};

\end{tikzpicture}
\end{center}

Answer 1

You can draw these with \rules and tabulars for the structural layout:

\documentclass{article}

\begin{document}

Consider the following partition:
\begin{center}
  \begin{tabular}{ c @{\quad} c @{\quad} l }
    \makebox[2em]{$I_1$}\makebox[6em]{$I_2$} \\[-.4\normalbaselineskip]
    \rule[.5ex]{2em}{.4pt}\rule{.4pt}{1ex}\hspace{-.4pt}\rule[.5ex]{6em}{.4pt} &
      $\rightarrow$ & partition 1 \\
    \makebox[5.5em]{$I'_1$}\makebox[2.5em]{$I'_2$} \\[-.4\normalbaselineskip]
    \rule[.5ex]{5.5em}{.4pt}\rule{.4pt}{1ex}\hspace{-.4pt}\rule[.5ex]{2.5em}{.4pt} &
      $\rightarrow$ & partition 2
  \end{tabular}
\end{center}

We note that $I_1 \subset I'_1$ and $I'_2 \subset I_2$. Thus,
\begin{center}
  \begin{tabular}{ l @{\quad} c @{\quad} c }
    & & \makebox[2em]{$I_1$}\makebox[3.5em]{$I^B_2$}\makebox[2.5em]{$I^A_2$} \\[-.4\normalbaselineskip]
    partition 1 becomes & $\rightarrow$ & 
      \rule[.5ex]{2em}{.4pt}\rule{.4pt}{1ex}\hspace{-.4pt}\rule[.5ex]{3.5em}{.4pt}\rule{.4pt}{1ex}\hspace{-.4pt}\rule[.5ex]{2.5em}{.4pt} \\
    & & \makebox[2em]{$I^{\prime A}_1$}\makebox[3.5em]{$I^{\prime C}_1$}\makebox[2.5em]{$I'_2$} \\[-.4\normalbaselineskip]
    partition 2 becomes & $\rightarrow$ &
      \rule[.5ex]{2em}{.4pt}\rule{.4pt}{1ex}\hspace{-.4pt}\rule[.5ex]{3.5em}{.4pt}\rule{.4pt}{1ex}\hspace{-.4pt}\rule[.5ex]{2.5em}{.4pt}
  \end{tabular}
\end{center}

\end{document}