Final answer:
The statement is false; the presence of IPTG causes the Lac repressor to release from the Operator DNA, not preferentially bind to it. In the presence of inducers like lactose or IPTG, the repressor's hold on the Operator is released, allowing transcription.
Step-by-step explanation:
The statement that the Lac repressor bound to IPTG prefers Operator DNA 10,000 times more than non-Operator DNA is False. IPTG is an inducer that binds to the Lac repressor, causing it to change shape and release from the Operator DNA. Thus, when IPTG is present, the repressor does not preferentially bind Operator DNA; it is prevented from binding altogether.
IPTG acts as an analog of allolactose, a natural inducer of the lac operon. When lactose is present in the growth medium, its derivative allolactose binds to the Lac repressor, leading to a similar result as IPTG: the repressor can no longer bind to the Operator sequence effectively, allowing RNA polymerase to transcribe the operon. The I gene product, the repressor protein, is free to bind the Operator site and inhibit transcription in the absence of an inducer like lactose or IPTG, keeping the operon "OFF by default." However, when lactose or IPTG is present, it binds the repressor, releasing it from the operator, allowing transcription to proceed.