Final answer:
The density of the air inside the glass will remain the same at the surface.
Step-by-step explanation:
When you hold a glass full of air upside down and take it to the bottom of a swimming pool without tipping it, the density of the air inside the glass will remain the same at the surface. This is because density does not change with depth in a static fluid. The pressure at any point in a static fluid depends only on the depth at that point, not on the density of the fluid. In the case of a swimming pool, the density of the water is approximately constant, so the density of the air inside the glass will also be constant at the surface.