Display ads purchased with Amazon DSP can run on Amazon-owned inventory and third-party inventory in both desktop and mobile environments.

The correct answer is True because Amazon's Demand-Side Platform (DSP) allows advertisers to purchase display ads that can run on both Amazon-owned inventory, such as Amazon's website and apps, as well as third-party inventory through various external websites and apps. This means that ads can be displayed not only across Amazon’s own ecosystem but also on other websites and mobile environments that participate in Amazon’s advertising network. This broadens the reach of display ads purchased through Amazon DSP, making them visible to a larger audience across desktop and mobile devices, enhancing targeting options and campaign effectiveness.