Are the following statements true or false?

? True False  1. $\int_C \vec{F} \cdot d\vec{r} = f(Q) - f(P)$ whenever $P$ and $Q$ are the endpoints of the curve $C$.

? True False  2. If $\vec{F}$ is path-independent, then there is a potential function for $\vec{F}$.

? True False  3. If $\int_C \vec{F} \cdot d\vec{r} \not= 0$ for some closed path $C$, then $\vec{F}$ is path dependent.

? True False  4. If $\vec{F}$ is path-independent and $C$ is any closed curve, then $\int_C \vec{F} \cdot d\vec{r} = 0$.

? True False  5. If the vector fields $\vec{F}$ and $\vec{G}$ have $\int_C \vec{F} \cdot d\vec{r} = \int_C \vec{G} \cdot d\vec{r}$ for a particular path $C$, then $\vec{F} = \vec{G}$.

? True False  6. If $\int_C \vec{F} \cdot d\vec{r} = 0$ for one particular closed path, then $\vec{F}$ is path-independent.

? True False  7. If $\vec{F} = \nabla f$, then $\vec{F}$ is conservative.

? True False  8. The circulation of any vector field $\vec{F}$ around any closed curve $C$ is zero.