MathDB

Let

A

be a given finite set with some of its subsets called pretty. Let a subset be called small, if it's a subset of a pretty set. Let a subset be called big, if it has a pretty subset. (A set can be small and big simultaneously, and a set can be neither small nor big.) Let

a

denote the number of elements of

A

, and let

p

s

and

b

denote the number of pretty, small and big sets, respectively. Prove that

2^a\cdot p\le s\cdot b

.
Proposed by András Imolay, Budapest

Problem Statement