Here is a simple puzzle to develop your understanding and intuition.
You are faced with a problem in which you need to make a decision. For example, you might be choosing $u_0$. You can choose $u_0=0$ or $u_0=1$. One of these is optimal.
There is something "A" which you do not know. It could be either true or false.
If A is true then $u_0=1$ is definitely optimal (i.e. better than $u_0=0$).
If A is false then $u_0=1$ is also definitely optimal.
Can you therefore conclude that $u_0=1$ is optimal?
Thus
You are faced with a problem in which you need to make a decision. For example, you might be choosing $u_0$. You can choose $u_0=0$ or $u_0=1$. One of these is optimal.
There is something "A" which you do not know. It could be either true or false.
If A is true then $u_0=1$ is definitely optimal (i.e. better than $u_0=0$).
If A is false then $u_0=1$ is also definitely optimal.
Can you therefore conclude that $u_0=1$ is optimal?
Thus
