MathDB

Let

(m,r,s,t)

be positive integers such that

m\geq s+1

and

r\geq t

. Consider

m

sets

A_1, A_2, \dots, A_m

with

r

elements each one. Suppose that, for each

1\leq i\leq m

, there exist at least

t

elements of

A_i

, such that each one(element) belongs to (at least)

s

sets

A_j

where

j\neq i

. Determine the greatest quantity of elements in the following set

A_1 \cup A_2 \cup A_3 \dots \cup A_m

3