The lac operon is negatively regulated because the lac repressor binds when lactose is absent, and no gene expression then occurs. The genes are turned off (negative/off). In contrast, the trp operon is turned on in the absence of tryptophan (positive/on).
Work Step by Step
The key here is see that negative regulation involves the turning off of genes by a regulatory protein when their expression is not needed while positive regulation involves turning on by a protein when expression of those genes is needed.