investment opportunities

1. Show that a preference relation represented by a utility function has to satisfy completeness and transitivity.
2. You have a choice between two investment opportunities. One pays $20,000 with certainty, while the other pays $30,000 with probability 0.2, $6,000 with probability 0.4, and $1,000 with probability 0.4. Your utility is of the type U(x) = x? , 0