Problem
COM-B1-M04-P016 Nested Pairs of Subsets
#16
★★★☆☆ Level 3 of 5
How many pairs \((A,B)\) of subsets of an \(n\)-element set satisfy \(A\subset B\)?
Each element has three states.
Each element is either outside \(B\), in \(B\) but not in \(A\), or in both sets. Three independent states for each of \(n\) elements give \(3^n\) pairs.
Strong encoding of the object element by element.