Let the universe U be the set of all living human beings, and F be the binary relation over U such that its intended meaning is the following: for any x, y U, xF y if and only if x is the father of y.

1- Then, answer whether the following proposition is true or false. For any x, y, z U, xF y & yFz xF z.

2- Let R be a rational weak preference relation, P be the strict preference part of R, and I be the indifference part of R. Prove the following proposition: For any x, y, z U, xP y & yRz xP z.