Question

how does lac operon show negative regulation??

Answer 1

Lac operon consists of four genes LacZ, Lacy, LacA and LacI. Genes Z, Y and A are structural genes whereas LacI gene encodes for a repressor that in the absence of a inducer binds to the promoter of Lac operon to inhibit the transcription of the structural genes.
When there is no inducer (lactose) LacI gene encodes repressor to inhibit the transcription. This type of regulation is known as a negative regulation.