solution:
Given capacities are: f(x) = x2 – x and g(x) = 2|x – ½| – 1
At x = – 1
f(- 1) = 12 + 1 = 2 and g(- 1) = 2|-1 – ½| – 1 = 2
At x = 0
F(0) = 0 and g(0) = 0
At x = 1
F(1) = 0 and g(1) = 0
At x = 2
F(2) = 2 and g(2) = 2
So we can see that, for each a ∈ A , f(a) = g(a) This infers f and g are equivalent capacities.