ece108: add set ops

docs/1b/ece108.md

@@ -354,3 +354,40 @@ $$\overline S$$
 The **universal set** is the set containing everything, and is the complement of the empty set.
 
 $$\mathcal U=\overline\empty$$
+
+### Set operations
+
+A **subset** is inside another that is a **superset**.
+
+$$
+S\subseteq T \\
+S\subseteq T\iff \forall x\in\mathcal U,(x\in S\implies x\in T)
+$$
+
+A **strict or proper subset** is a subset that is not equal to its **strict or proper superset**.
+
+$$S\subset T$$
+
+Two sets are equal if they are subsets of each other.
+
+$$S=T\equiv (S\subseteq T)\wedge (T\subseteq S)$$
+
+The **union** of two sets is the set that contains any element in either set.
+
+$$S\cup T=\{x\in\mathcal U|(x\in S)\vee(x\in T)\}$$
+
+The **intersection** of two sets is the set that only contains elements in both sets.
+
+$$S\cap T=\{x\in\mathcal U|(x\in S)\wedge(x\in T)\}$$
+
+The **difference** of two sets is the set that contains elements in the first but not the second. The remainder is dropped.
+
+$$S-T=S\backslash T$$
+
+The **complementary** set is every element not in that set.
+
+$$
+\overline S=\{x:x\not\in S\} \\
+\overline S=\mathcal U-S
+$$
+