Pick out the correct equation relating 'F' and 'A'.

Answer: Option A

Here the $$F$$ is Gibbs free energy and $$A$$ is Helmholtz free energy.
So, $$F=H-TS$$   and $$A=U-TS$$
$$\begin{array}{rl}& \Rightarrow F=H+A-U\\ & \Rightarrow F=A+PV\end{array}$$