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\exercise*[0.3.6]
\begin{enumerate}[label=\emph{\alph*)}]
    \item Wanting to show:
        $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$

        In order to prove this equivalence, we have to prove the implication both ways. We use two lemmas for this.

        \begin{lemma}[test]
            $A \cap (B \cup C) \implies (A \cap B) \cup (A \cap C)$

            Let $x \in A \cap (B \cup C)$.
        \end{lemma}
        \begin{definition}
            Test.
        \end{definition}
    \item
\end{enumerate}

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