Is Air There?

First, I put a plastic bag over a glass cup. Then I rubber banded the bag to the cup. I pushed the bag in and it was hard. Then when I got it in. Then I tried to pull the bag out and it was hard too. The reason this happened is the air pressure was higher on the inside when I tried to push it in. Once it was pushed in, the air pressure was lower and it raised on the outside. So it was hard to pull out.