User:Quantumdude/Sandbox


 * $$A \subseteq A\,\!$$
 * $$A \subseteq B\,\!$$ and $$B \subseteq A\,\!$$ if and only if $$A = B\,\!$$
 * If $$A \subseteq B\,\!$$ and $$B \subseteq C\,\!$$, then $$A \subseteq C\,\!$$
 * $$\varnothing \subseteq A \subseteq S\,\!$$
 * $$A \subseteq A \cup B\,\!$$
 * If $$A \subseteq C\,\!$$ and $$B \subseteq C\,\!$$, then $$A \cup B \subseteq C\,\!$$
 * $$A \cap B \subseteq A\,\!$$
 * If $$C \subseteq A\,\!$$ and $$C \subseteq B\,\!$$, then $$C \subseteq A \cap B\,\!$$
 * $$A \subseteq B\,\!$$
 * $$A \cap B = A\,\!$$
 * $$A \cup B = B\,\!$$
 * $$A \setminus B = \varnothing$$
 * $$B^C \subseteq A^C$$
 * $$C \setminus (A \cap B) = (C \setminus A) \cup (C \setminus B)\,\!$$
 * $$C \setminus (A \cup B) = (C \setminus A) \cap (C \setminus B)\,\!$$
 * $$C \setminus (B \setminus A) = (A \cap C)\cup(C \setminus B)\,\!$$
 * $$(B \setminus A) \cap C = (B \cap C) \setminus A = B \cap (C \setminus A)\,\!$$
 * $$(B \setminus A) \cup C = (B \cup C) \setminus (A \setminus C)\,\!$$
 * $$A \setminus A = \varnothing\,\!$$
 * $$\varnothing \setminus A = \varnothing\,\!$$
 * $$A \setminus \varnothing = A\,\!$$
 * $$B \setminus A = A^C \cap B\,\!$$
 * $$(B \setminus A)^C = A \cup B^C\,\!$$
 * $$U \setminus A = A^C\,\!$$
 * $$A \setminus U = \varnothing\,\!$$