I am trying to understand which of the two operons uses positive and which uses negative feedback. In addition, which of the two are an inducible and which is a repressible system. Would someone mind explaining that?

Most operons - including the E. coli lac and trp operons - in bacteria are regulated negatively through the action of repressor proteins; this can be achieved through both induction and repression. So a repressor protein can either keep a gene inactive or switch it off if it's active - both occur through the action of a repressor, hence these systems are characterised as being negatively regulated.

The lac operon is an example of an inducible operon - a ligand inactivates the repressor and induces gene expression.

The trp operom is an example of a repressible operon - a ligand activates the repressor and represses gene expression.

Edited February 8, 201312 yr by Zwirko

it is also a bit a matter of perspective. In these cases they are inducible or repressible by a given substrate. The mechanism in both cases is, as mentioned, is based on repression by a transcription factor.

Most metabolic operons appear to be negatively regulated indeed. However, although it could also be that activators (proteins as well as sRNAs) are somewhat harder to detect.

Awesome explanation. Now it makes sense where inductive and repressive come from-- the relationship between substrate and repressor. But wouldn't you say that the lac is neg feedback because an excess of lactose would inhibit the system. However the trp would be positive feedback where an excess of substrate would keep the system active?