What offense is committed when a man uses aerosol paint to write on a building?

The offense committed when a man uses aerosol paint to write on a building is classified as graffiti. Graffiti specifically refers to markings or drawings made on public or private property without the owner's consent, typically using spray paint, markers, or other similar mediums. In this context, the act of writing on a building with aerosol paint fits the definition of graffiti, as it involves creating unauthorized artwork or inscriptions on a structure.

While vandalism is often associated with graffiti, it is a broader term that encompasses various acts of damaging or defacing property. Graffiti is a specific form of vandalism that highlights artistic expression using spray paint, thus making it the precise categorization for this scenario. The term destruction of property implies more significant damage or alteration than simply writing on a surface, and public mischief relates to actions that cause public disturbance or annoyance but do not necessarily involve property damage. Hence, graffiti is the most accurate description of the offense in this case.