Logic and sets · Power set · Subset versus element · Foundation
Find all three-element sets \(A\) with the following two properties:
(i) the set \(A\) has at least two elements in common with its power set \(\mathcal{P}(A)\);
(ii) \(3 \in A\).
(It is understood that no set is an element of itself, nor an element of its own element.)
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Municipal Competition 2020, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source