PERT Chart exercise - is there enough information to solve?
I don't know if there is a standard method to identify which activity matches which arrow, but I was able to complete your PERT chart by examining a few possible cases, while filling the chart from left to right. Each case was accepted or rejected after a while. I found that the higher arrow matches B and the lower C. Note that if you try to match C with the higher arrow, (2,3), E will match with the (3,5) arrow but then you will face the problem that only one activity depends on E while there are two arrows starting from it that have to be filled. Otherwise, if you match (2,3) with B, (3,5) will match with D and then there are two acivities dependent from D as you wish. More uncertainties will raise but they are solvable by considering the different cases.

So the information provided are enough to solve the excersise. One possible typing error that I identify in the problem statement is that Q doesn't depend on K, L and P only, but it depeds on M too. That's why there are four arrows entering node 15 instead of three. Otherwise there is no lack of information and you can solve the problem as I described above.

A second way to solve the problem is to create the PERT chart based on the data written in the table by yourself. The graph that you will make will be isomorphic with the graph that you will get if you merge the nodes connected by dotted edges on the graph of the problem statement. So after that you will have to create an edge matching between the two graphs in order to find which activity matches which arrow on the given graph.

Both methods will lead to a correct solution, you can try them for practice.