\documentclass[a4paper]{article}
%\usepackage[czech]{babel}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amssymb,amsmath}
%\usepackage{hyperref}

\newtheorem{exercise}{Exercise}[section]

\input ../macros

\input ../MNCMPpagesaving.tex

\newdimen\tmpd
\newbox\verbbox

\setcounter{section}{3}
%=====================================================
\begin{document}

\textit{Homework from Fuzzy Logic.
%Choose the basic or advanced level.
}

\bigskip
%\textbf{Basic level}

Exercise from fuzzy intersections.

\begin{exercise}
Fuzzy sets $A,B$ have the following vertical representations:
\begin{align*}
\mu_A(x)=
\begin{cases}
 1\,, & x\in [9,11]\,,\\
 \dfrac{x-6}3\,, & x\in [6,9]\,,\\
 12-x\,, & x\in [11, 12]\,,\\
0\,, & \text{otherwise}\,,\\
\end{cases}
\\
\mu_B(x)=
\begin{cases}
 1\,, & x\in [10,11]\,,\\
 \dfrac{x-7}3\,, & x\in [7,10]\,,\\[.5em]
 \dfrac{13-x} 2\,, & x\in [11, 13]\,,\\
0\,, & \text{otherwise}\,.\\
\end{cases}
\end{align*}

Find their standard, product, and \L ukasiewicz intersections.
\end{exercise}
\end{document}
