Fluid statics - buoyancy force problem 

The pictures above show the question and soution. The part I don't understand is why the air pressure is acting upwards against the plate instead of downwards on the water. Could someone explain this please.
 A: 
The part I don't understand is why the air pressure is acting upwards against the plate instead of downwards on the water.   

The pressure is acting in all directions and so there is a upward force on the plate and a downward force on surface of the the water.  
This means that the pressure on top of the water is becoming larger as air is introduced into the chamber.  
The pressure on the top of the block and the pressure at the bottom of the block increases by the same amount.
Thus the pressure difference between the top and bottom of the block, which is responsible for the upthrust, stays the same.
There is no change in the upthrust on the block as a result of the air pressure inside the chamber increasing.
A: The air pressure is acting in all directions. It pushes on the water, the sides of the tank, the plate, and the mercury in the manometer. But the tank is rigid, and water is virtually incompressible, and has nowhere to go, so the air pressure has no effect on the tank nor the water. So in this setup, only the mercury and the plate can move.
