MathDB

Let

S

be a set with 10 distinct elements. A set

T

of subsets of

S

(possibly containing the empty set) is called union-closed if, for all

A, B \in T

, it is true that

A \cup B \in T

. Show that the number of union-closed sets

T

is less than

2^{1023}

.
Proposed by Tony Wang

Problem Statement