'Operon model' for gene regulation in bacteria was proposed by

Define an operon, giving an example, explain an Inducible operon.

How many of the given statements $(i-iv)$ is/are correct?

$i.$ In transcription, adenosine pairs with uracil.

$ii.$ Regulation of lac operon by repressor is referred to as positive regulation.

$iii.$ The human genome has approximately $50,000\; genes.$

$iv. $ Haemophilia is a sex-linked recessive disease.

Definitions/Explanation : Splicing & Operator gene
 

In the medium where $E$. coli was growing, lactose was added, which induced the lac operon. Then, why does lac operon shut down some time after addition of lactose in the medium?