It can be explained with the help of base-pair complementary rule which states that adenine will always base-pair with thymine and guanine will always base-pair with cytosine.
Adenine bonds with thymine through two hydrogen bonds and guanine bonds with cytosine through three hydrogen bonds.
Allolactose is an example of an inducer, a small molecule that triggers expression of a gene or operon. The lac operon is considered an inducible operon because it is usually turned off (repressed), but can be turned on in the presence of the inducer allolactose.