diff --git a/docs/1b/ece108.md b/docs/1b/ece108.md index 121202b..fbece62 100644 --- a/docs/1b/ece108.md +++ b/docs/1b/ece108.md @@ -395,6 +395,10 @@ $$ \overline S=\mathcal U-S $$ +The intersection and union operators have the same properties as **AND** and **OR** and so are equally commutative / associative. + +**De Morgan's laws** still hold with sets. + ### Intervals An interval can be represented as a bounded set. @@ -402,3 +406,23 @@ An interval can be represented as a bounded set. $$[a,b)=\{x\in\mathcal U|a\leq x\wedge x = \left\iff (a=c)\wedge(b=d)$$ + +The **Cartesian product** of two sets is the set of all ordered pair combinations within the two sets. + +$$A\times B=\{\left | (a\in A)\wedge (b\in B)\}$$ + +It is effectively the cross product, so is not commutative, although distributing unions, intersections, and differences works as expected. + +The **n-Cartesian product** of $n$ sets expands the Cartesian product. + +$$A\times B\times\dots\times Z=\{\left|a\in A, b\in B,\dots,z\in Z\}$$