In the $lac$ operon, what does the term "$lac$" refer to?

Mark the incorrect option with respect to the $lac$ operon.

The switching on and off of the $lac$ operon is regulated by which of the following?

Which of the following statements concerning the regulatory gene $(i)$,associated with the $lac$ operon are incorrect?
$(I.)$ $\text{mRNA}$ is transcribed from the $i$ gene whether lactose is present or not.
$(II.)$ $\text{mRNA}$ is transcribed from the $i$ gene only when the lactose is present.
$(III.)$ $\text{mRNA}$ is transcribed from the $i$ gene only when the lactose is not present.
$(IV.)$ Lactose inhibits the translation of $i$ gene $\text{mRNA}$.

In the $lac$ operon model,lactose molecules function as:

Why can glucose and galactose not act as inducers for the $lac$ operon?