Final answer:
The statement is false; Progressive Rock is characterized by long, complex compositions that are not primarily designed for short radio airplay formats.
Step-by-step explanation:
The statement that Progressive Rock bands tend to write their music with radio airplay in mind, and that Prog songs are, for the most part, short and catchy, is FALSE. Progressive Rock, often referred to as Prog Rock, is known for its extended compositions, complex time signatures, and conceptual album structures. The genre typically leans towards musical experimentation and sophistication over conventional pop song structures aimed at mass market appeal, which is often a requirement for radio airplay. It's not uncommon for Progressive Rock songs to extend well beyond the typical three-minute radio standard, with some tracks even spanning the length of an entire album side.