Graphs on diagrams and on equipotence

Could someone help me to make the following graphs. Thanks.

What I tried for the diagrams was the following,

 \begin{center}
\begin{tikzpicture}
\draw (-3.3,-0.4)node[right] {$1$};
\draw (-3.3,-0.8)node[right] {$2$};
\draw (-3.3,-1.2)node[right] {$3$};
\draw (-3.3,-1.6)node[right] {$4$};
\draw (-3.2222,-2)node[right] {$\vdots$};
\draw (-3.2222,-2.4)node[right] {$\vdots$};
\draw (-3.6,-3) node[right] {$n-1$};
\draw (-3.3,-3.4) node[right] {$n$};
\draw (-0.3,-0.4)node[right] {$a_1$};
\draw (-0.3,-0.8)node[right] {$a_2$};
\draw (-0.3,-1.2)node[right] {$a_3$};
\draw (-0.3,-1.6)node[right] {$a_4$};
\draw (-0.2222,-2)node[right] {$\vdots$};
\draw (-0.2222,-2.4)node[right] {$\vdots$};
\draw (-0.3,-3) node[right] {$a_{n-1}$};
\draw (-0.3,-3.4) node[right] {$a_n$};

\draw (2.6,-0.4)node[right] {$b_1$};
\draw (2.6,-0.8)node[right] {$b_2$};
\draw (2.6,-1.2)node[right] {$b_3$};
\draw (2.6,-1.6)node[right] {$b_4$};
\draw (2.7,-2)node[right] {$\vdots$};
\draw (2.7,-2.4)node[right] {$\vdots$};
\draw (2.6,-3) node[right] {$b_{n-2}$};
\draw (2.6,-3.4) node[right] {$b_{n-1}$};
\draw (-3,-2) ellipse (1cm and 2cm);
\draw (-3.1,0.3) node {$J_n$};
\draw (0,-2) ellipse (1cm and 2cm);
\draw (-0.1,0.3) node {$A$};
\draw (3,-2) ellipse (1cm and 2cm);
\draw (2.8,0.3) node {$B$};
\draw [->](-2,0) -- (-1,0);
\draw (-1.5,0.3) node {$\phi$};
\draw[->](1,0) -- (2,0);
\draw (1.5,0.3) node {$f$};
\draw[->] (-3,-0.4) -- (-0.2,-2.9);
\end{tikzpicture}
\end{center}


Which threw me the following graph (I made it with three diagrams)

The issue is that they are too large and I do not know how to make those points of the diagrams. I don't how to draw one similar to the third graph.

• Well what have you tried? Jun 26, 2021 at 5:28
• You can look at my edit. @M.A.Bromuela Jun 26, 2021 at 5:42
• Nicely done, it's great that you've shown us what you've done so far :) hopefully someone will be able to help Jun 26, 2021 at 6:42
• Are dots necessary? The one in the example graphs? Jun 26, 2021 at 6:44
• Well, if they are necessary. I would like to know how they are put, to take it into account in future graphics. @M.A.Bromuela Jun 26, 2021 at 7:33

Okay tried to replicate the way according to the example. For the first problem, you may define dots with filldraw command and make circle dots of size 1pt. And I assume you know how to draw arrows already. I changed the appearance of the arrow tip using latex'. For the second problem, I used a separate standalone document to show how the graphic appears with the code. You can resize them with the resize command but it also makes the letters appear smaller, so be warned.

For the first problem:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{arrows}

\begin{document}

\begin{center}
\begin{tikzpicture}
\draw[thick] (-3,-1.9) ellipse (1.1cm and 1.875cm);
\filldraw[black] (-2.765,-0.4) circle (1pt) node[anchor=east] {$1$};
\filldraw[black] (-2.765,-0.8) circle (1pt) node[anchor=east] {$2$};
\filldraw[black] (-2.765,-1.2) circle (1pt) node[anchor=east] {$3$};
\filldraw[black] (-2.765,-1.6) circle (1pt) node[anchor=east] {$4$};
\draw (-2.79,-2) node[anchor=east] {$\vdots$};
\draw (-2.79,-2.4) node[anchor=east] {$\vdots$};
\filldraw[black] (-2.765,-3) circle (1pt) node[anchor=east] {$n-1$};
\filldraw[black] (-2.765,-3.4) circle (1pt) node[anchor=east] {$n$};

\draw[thick] (0.1,-1.9) ellipse (1.1cm and 1.875cm);
\filldraw[black] (-0.36,-0.4) circle (1pt) node[anchor=west] {$a_1$};
\filldraw[black] (0.6,-0.4) circle (1pt);
\filldraw[black] (-0.36,-0.8) circle (1pt) node[anchor=west] {$a_2$};
\filldraw[black] (0.6,-0.8) circle (1pt);
\filldraw[black] (-0.36,-1.2) circle (1pt) node[anchor=west] {$a_3$};
\filldraw[black] (0.6,-1.2) circle (1pt);
\filldraw[black] (-0.36,-1.6) circle (1pt) node[anchor=west] {$a_4$};
\filldraw[black] (0.6,-1.6) circle (1pt);
\draw[black] (-0.1,-2) node[anchor=west] {$\vdots$};
\draw[black] (-0.1,-2.4) node[anchor=west] {$\vdots$};
\filldraw[black] (-0.36,-3) circle (1pt) node[anchor=west] {$a_{n-1}$};
\filldraw[black] (0.6,-3) circle (1pt);
\filldraw[black] (-0.36,-3.4) circle (1pt) node[anchor=west] {$a_n$};
\filldraw[black] (0.6,-3.4) circle (1pt);

\draw[thick] (3.2,-1.9) ellipse (1.1cm and 1.875cm);
\filldraw[black] (2.8,-0.4) circle (1pt) node[anchor=west] {$b_1$};
\filldraw[black] (2.8,-0.8) circle(1pt) node[anchor=west] {$b_2$};
\filldraw[black] (2.8,-1.2) circle(1pt) node[anchor=west] {$b_3$};
\filldraw[black] (2.8,-1.6) circle(1pt) node[anchor=west] {$b_4$};
\draw (3,-2) node[anchor=west] {$\vdots$};
\draw (3,-2.4) node[anchor=west] {$\vdots$};
\filldraw[black] (2.8,-3) circle(1pt) node[anchor=west] {$b_{n-2}$};
\filldraw[black] (2.8,-3.4) circle(1pt) node[anchor=west] {$b_{n-1}$};

\draw (-3,0.3) node {$J_n$};
\draw (-0.1,0.3) node {$A$};
\draw (3.2,0.3) node {$B$};
\draw [->](-2,0) -- (-1,0);
\draw (-1.5,0.3) node {$\phi$};
\draw[->](1,0) -- (2,0);
\draw (1.5,0.3) node {$f$};

\draw[thick, -latex'] (-2.7,-0.4) -- (-0.35,-0.4);
\draw[thick, -latex'] (-2.7,-0.8) -- (-0.35,-0.8);
\draw[thick, -latex'] (-2.7,-1.2) -- (-0.35,-1.2);
\draw[thick, -latex'] (-2.7,-1.6) -- (-0.35,-1.6);
\draw[thick, -latex'] (-2.7,-3) -- (-0.355,-3);
\draw[thick, -latex'] (-2.7,-3.4) -- (-0.35,-3.4);

\draw[thick, -latex'] (0.7,-0.4) -- (2.7,-1.2);
\draw[thick, -latex'] (0.7,-0.8) -- (2.7,-3);
\draw[thick, -latex'] (0.7,-1.2) -- (2.7,-0.4);
\draw[thick, -latex'] (0.7,-1.6) -- (2.7,-0.8);
\draw[thick, -latex'] (0.7,-3) -- (2.7,-1.6);
\draw[thick, -latex'] (0.7,-3.4) -- (2.7,-3.4);
\end{tikzpicture}
\end{center}

\end{document}


For the second problem:

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{arrows}

\begin{document}
\begin{tikzpicture}
\foreach \x in {1,...,16}
\draw[shift={(\x,0)},color=black] (0pt,0.5pt) -- (0pt,0pt) node[anchor=south] {$\x$};
\draw[black,thick, latex-latex] (0,0) -- (17,0);
\foreach[evaluate={\j=int{\x+5}}] \x in {-7,...,8}{\draw[shift={(\j,-3)},color=black] (0pt,0.5pt) -- (0pt,0pt) node[anchor=north] {$\x$};};
\draw[black,thick, latex-latex] (-3,-3) -- (15,-3);
%\draw[shift={(\x,-3)},color=black] (0pt,0.5pt) -- (0pt,0pt) node[anchor=south] {$\x$};

\draw[thick, -latex'] (4,0) -- (4,-3);
\draw[thick, -latex'] (2,0) -- (5,-3);
\draw[thick, -latex'] (16,0) -- (-2,-3);
\draw[thick, -latex'] (14,0) -- (-1,-3);
\draw[thick, -latex'] (12,0) -- (0,-3);
\draw[thick, -latex'] (10,0) -- (1,-3);
\draw[thick, -latex'] (8,0) -- (2,-3);
\draw[thick, -latex'] (6,0) -- (3,-3);
\draw[thick, -latex'] (15,0) -- (13,-3);
\draw[thick, -latex'] (13,0) -- (12,-3);
\draw[thick, -latex'] (11,0) -- (11,-3);
\draw[thick, -latex'] (9,0) -- (10,-3);
\draw[thick, -latex'] (7,0) -- (9,-3);
\draw[thick, -latex'] (5,0) -- (8,-3);
\draw[thick, -latex'] (3,0) -- (7,-3);
\draw[thick, -latex'] (1,0) -- (6,-3);
\end{tikzpicture}
\end{document}


• I really didn't gave the time for the alignments. You may also try shortening the code for the second problem for drawing the arrows, perhaps with foreach with evaluate option. But I hope that sums this up. Jun 26, 2021 at 9:09
• Thank you very much, it is very helpful. Thank you for taking the time to help me with this. Jun 26, 2021 at 20:36