Prove that if a, b, x, y are real numbers such that
|x - a| < 1, |y - b| < 2, |a - b| > 7.
Then |x - y| > 4.
Suppose that the functions f, g are defined on a set containing A as a subset, then
sup_{A}(f + g) ≤ sup_{A} f + sup_{A} g.
Give an example that shows that "<" may happen.