TITLE: Renaud-Sarvate limitation on Frankl's Conjecture
QUESTION [9 upvotes]: I was wondering if someone could give me a specific example of union closed family with a three element set, none of whose elements are in half the members of the family. 
Thanks in advance!

REPLY [8 votes]: This example with minimal size $3$ is from D. G. Sarvate and J-C. Renaud, "Improved bounds for the union-closed sets conjecture", Ars Combinatoria 29 (1990), pp. 181-185:
$\mathcal A=\{A_1,\dots,A_{27}\},$ with
$A_1=\{1,2,3\}$
$A_2=\{1,2,3,6,7,8,9\}$
$A_3=\{1,2,3,4,6,7,8,9\}$
$A_4=\{1,2,3,4,5,6,7,8,9\}$
$A_5=\{1,2,3,4,5,8,9\}$
$A_6=\{1,2,3,4,5,6,8,9\}$
$A_7=\{1,2,3,4,5,6,7\}$
$A_8=\{1,2,3,4,5,6,7,8\}$
$A_9=\{6,7,8,9\}$
$A_{10}=\{4,6,7,8,9\}$
$A_{11}=\{4,5,6,7,8,9\}$
$A_{12}=\{4,5,8,9\}$
$A_{13}=\{4,5,6,8,9\}$
$A_{14}=\{4,5,6,7\}$
$A_{15}=\{4,5,6,7,8\}$
$A_{16}=\{1,6,7,8,9\}$
$A_{17}=\{1,4,6,7,8,9\}$
$A_{18}=\{1,4,5,6,7,8,9\}$
$A_{19}=\{2,4,5,8,9\}$
$A_{20}=\{2,4,5,6,8,9\}$
$A_{21}=\{2,4,5,6,7,8,9\}$
$A_{22}=\{3,4,5,6,7\}$
$A_{23}=\{3,4,5,6,7,8\}$
$A_{24}=\{3,4,5,6,7,8,9\}$
$A_{25}=\{1,2,4,5,6,7,8,9\}$
$A_{26}=\{1,3,4,5,6,7,8,9\}$
$A_{27}=\{2,3,4,5,6,7,8,9\}$  
Here $A_1=\{1,2,3\}$ is the unique set of minimal size, and each of the elements $1,2,3$ is in exactly $13$ of the $27$ sets.