Seven buildings are located in an urban development.
Three of the buildings are residential; the other four are commercial.
Each of the residential buildings is made of either brick or wood.
Each of the commercial buildings is made of either wood, concrete, brick, or steel.
All of the residential buildings and all of the brick buildings have fire escapes, but no other buildings do.
Exactly four of the buildings have fire escapes.
If exactly half of the buildings with fire escapes are wooden, then which one of the following must be false?