diff --git a/docs/1b/ece108.md b/docs/1b/ece108.md index 9c34c89..9c7af5e 100644 --- a/docs/1b/ece108.md +++ b/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. + +$$ +\overline S=\{x:x\not\in S\} \\ +\overline S=\mathcal U-S +$$ +