A collection of non-empty subsets of the set {1, 2, . . . , n} is called a simplex if, whenever a subset S is included in the collection, any non empty subset T of S is also included in the collection. Only one of the following collections of subset of { 1, 2, . . . , n } is a simplex. Which one is it?
(A) The collection of all subsets S with the property that one belongs to S;
(B) The collection of all subsets having exactly 4 elements;
(C) The collection of all non-empty subsets which do not contain any even number;
(D) The collection of all non-empty subsets except for the subset {1}.
