What area of mathematics is this problem asking about? A colleague posted this on a whiteboard (as a brain-teaser I guess):

A $\rightarrow$ B;
B $\rightarrow$ C;
AD $\rightarrow$ E;
BE $\rightarrow$ C;
BF $\rightarrow$ D;
AC $\rightarrow$ F
What is the minimum set I need to determine A, B, C, D, E, and F?

I'm not interested in help solving the problem.  I'd just like to know the general domain of the problem because it's not clear to me.  It probably is clear to a mathematics community.
For example, does it deal with set theory, or logic?  Or some other area of math?
 A: It's logic. A-F are either true or false, and the question is which ones you need to know (at a minimum) to determine the truth of all six of them.
Edit: AB means "A and B," the arrow is implication. 
A: 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 
words.
Without more explanation from your colleague, I don't think the question can be reasonably answered.
