Final answer:
The statement is true: prokaryotes use a single core RNA polymerase modified by different sigma subunits for transcription, whereas eukaryotes employ three distinct RNA polymerases for different genes.
Step-by-step explanation:
The statement is true: Unlike eukaryotes, which use three different RNA polymerases, prokaryotes use only one type of core RNA polymerase molecule but modify it with different sigma subunits. In eukaryotic organisms, distinct RNA polymerases (RNA polymerases I, II, and III) transcribe different subsets of genes. Each of these eukaryotic polymerases also requires a distinct set of transcription factors to initiate transcription.
In contrast, prokaryotes like E. coli use a single RNA polymerase to transcribe all of their genes. This polymerase is composed of four core subunits α, α, β, and β' that assemble into the core enzyme. The additional sigma (σ) subunit is responsible for transcription initiation, enabling the polymerase to identify the correct initiation sites on the DNA. Without the sigma subunit, the core enzyme would not have specificity, leading to random and non-functional mRNA molecules.