For a vector field $\vec{F}$, which of the following statements are true?

I.If $\vec{F}$ is path independent, then the $\vec{F}$ is conservative.II.If $\vec{F}$ has a potential function, then $\vec{F}$ is conservative.III.If the line integral $\displaystyle \int_C \vec{F} ds = 0$ for some simple closed curve $C$, then $\vec{F}$ is conservative.IV.If the curl of $\vec{F}$ is zero, then $\vec{F}$ is conservative.