Set Exercises
Why
Here are some exercises on sets.1
\begin{exercise} Let $A, B, C$ denote sets. Show $((A \cap B) \cup C = A \cap (B \cup C)) \iff (C \subset A)$ Observe that the condition does not involve $B$. \end{exercise}
\begin{exercise}
\[
A - B = A \cap B'.
\]
\begin{exercise}
\[ A \subset B \text{ if and only if} A - B = \varnothing. \]
\end{exercise}\begin{exercise}
\[ A - (A - B) = A \cap B. \]
\end{exercise}\begin{exercise}
\[ A \cap (B - C) = (A \cap B) - (A \cap C). \]
\end{exercise}
\begin{exercise}
\[
(A \cap B) \subset ((A \cap C) \cup (A \cap C')).
\]
\begin{exercise}
\[ ((A \cup C) \cap (B \cup C')) \subset (A \cup B). \]
\end{exercise}\blankpage
- Future editions will give the hypotheses more clearly. ↩︎