Positive and negative regulation:

The lac operon is an excellent example of negative control or negative regulation of gene expression in which they bound repressor prevents transcription of the structural genes. The Positive control or positive regulation of gene expression is when the regulatory protein binds to increases and DNA the rate of transcription.  In that case the regulatory protein is known as an activator.  The CAP or CRP included in regulating the lac operon is a good instance of an activator. Therefore the lac operon is subject to both positive and negative control.