Exercise 2.35 (Functional Constraints). Find all functions satisfying the following conditions:

1 f(1, 0, 0, 0) = 1, f(0, 1, 1, 1) = 0;

2 f(1, 0, 0, 0) = 1, f linear in one or more variables;

3 f(0, 1, 0, 0) = f(1, 0, 1, 1), f symmetric (consider all possibilities);

4 f(1, 0, 0, 1) = 0, f self-dual