Let $X$ be uniform on $(0,1)$ and $Y:=3X+1$.

How that $X$ and $Y$ are not independent.

Clearly they are not independent since $Y$ is a function of $X$ but I don't know how to prov this formally. 

My notes give two ways: show that there are two event $\{X \leq s\}, \{Y \leq t\}$ that are not independent events or to show that the joint distribution function is not the product of the individual distribution functions. I don't really understand to be honest.