Economics question

Problem 1. Consider a probability space (S, F, P). You may assume that & is a finite set if you want. 1. Consider two sigma-fields G C F and H C F. Define the smallest o-field containing G and H, call it I. 2. Prove that such smallest o-field exists. 3. Find a simple example where F, G, H and I, are all different from each other, and no one is the trivial o-field (that is {0, 1})