Yes air takes up space
Glue a piece of cotton to the bottom of a clear, plastic cup. Then fill a bucket, or container larger than the cup, with water. Slowly lower the cup, open side first, into the bucket, making sure to keep it level. Remove the cup and the cotton
ball won't be wet!
That's one expeiment that shows air takes up space. If air didn't take up space, the water would have filled the space in the cup and made the cotton ball absorb the water (making it wet). Since air is matter and has mass, it takes up the space in the cup, thereby preventing the water from filling it up. the air would have to escape that space before the water could rush in i.e. tilting the cup once submerged, you will notice the bubbles rushing to the top of the water - this is the air escaping, allowing the water to rush in and take its place.