\[
\newcommand{\tr}{\Rightarrow}
\newcommand{\trs}{\tr^{\!\ast}}
\newcommand{\rlnm}[1]{\mathsf{(#1)}}
\newcommand{\rred}[1]{\xrightarrow{#1}}
\newcommand{\rreds}[1]{\mathrel{\xrightarrow{#1}\!\!^*}}
\newcommand{\cl}{\mathsf{Cl}}
\newcommand{\pow}{\mathcal{P}}
\newcommand{\matches}{\mathrel{\mathsf{matches}}}
\newcommand{\kw}[1]{\mathsf{#1}}
\newcommand{\andop}{\mathrel{\&\!\&}}
\newcommand{\orop}{\mathrel{\|}}
\newcommand{\ff}{\mathsf{false}}
\newcommand{\tt}{\mathsf{true}}
\newcommand{\abra}[1]{\langle #1 \rangle}
\newcommand{\bnfnt}[1]{\abra{\small \textsf{#1}}}
\newcommand{\llbracket}{[\![}
\newcommand{\rrbracket}{]\!]}
\newcommand{\first}{\mathsf{First}}
\newcommand{\nullable}{\mathsf{Nullable}}
\newcommand{\follow}{\mathsf{Follow}}
\newcommand{\tm}[1]{\mathsf{#1}}
\newcommand{\nt}[1]{\mathit{#1}}
\newcommand{\Coloneqq}{::=}
\newcommand{\abs}[1]{|#1|}
\]
-
\[\{ w \mid \text{$w$ is any word over $\{0,1\}$}\}\]
-
\[\{ w \mid \text{$w$ contains at least three letter 1} \}\]
-
\[\{ w \mid \text{$w$ starts and ends with the same symbol} \}\]
-
\[\{ w \mid \text{the length of $w$ is odd and its middle letter is $0$}\}\]
-
\[\{ w \mid \text{$w$ is a palindrome (i.e. the same word when reversed)}\}\]
-
\[\{uv \mid |u| = |v| \text{ and } u \neq v^R\}\]
(in the lecture, this last example accidentally had condition $u \neq v$)