Ex-2.9

Using the add-interval definition, for add-interval:

width(x+y) =  (upper-bound(x) + upper-bound(y))
            - (lower-bound(x) + lower-bound(y))
           = width(x) + width(y) 

Using the sub-interval definition, for sub-interval

width(x-y) = (upper-bound(x) - lower-bound(y))
           -(lower-bound(x) - upper-bound(y))
          = width(x) + width(y)