Question

Discrete Math:

Show that, (A-C) intersection (C-B) = the null set.

Answer 1

\[\begin{align}
x \in (A \setminus C) \cap (C \setminus B) &\iff x \in (A \setminus C) \land x \in (C \setminus B) \\
&\iff x \in A \land \underbrace{x \notin C \land x \in C}_{\bot} \land x \notin B \\
&\iff \bot.
\end{align}\]