I first interpreted this as a dependency graph, with $pq\to r$ meaning that if you know $p$ and $q$, then you can find $r$, or that tasks $p$ and $q$ are prerequisites for $r$, or something of that sort.
Understood this way, then it is a problem of graph theory, to find the source vertices of the directed graph determined by the given relations. There is one source, $A$, because from $A$ we can get to $B$ and to $C$; then from $AC$ we get to $F$; from $BF$ we get to $D$; and from $AD$ we get to $E$.
But I have no way to be sure that this is the intended interpretation. It might mean something completely different. For example, $pq\to r$ might mean that if $p$ and $q$ are riding in the same taxi then $r$ cannot ride there too, and the question is to find the minimum required number of taxis; then the answer is very different. Or it might be as Jonathan Christensen says, which is different again. Or perhaps $pq\to r$ means that whenever you have letters $p$ and $q$ adjacent in a word, you can replace them with $r$, and the question is to find the number of English words that transform into other English
Without more explanation from your colleague, I don't think the question can be reasonably answered.