Question 10
(GDR 1) Let $N=\{1,2,\ldots,n\}$, $n\ge2$. A collection $F=\{A_1,\ldots,A_t\}$ of subsets $A_i\subseteq N$, $i=1,\ldots,t$, is said to be separating if for every pair $\{x,y\}\subseteq N$, there is a set $A_i\in F$ such that $A_i\cap\{x,y\}$ contains just one element. A collection $F$ is said to be covering if every element of $N$ is contained in at least one set $A_i\in F$. What is the smallest value $f(n)$ of $t$ such that there is a set $F=\{A_1,\ldots,A_t\}$ that is simultaneously separating and covering?