1. [6 pts] Given the relation R( A, B, C, D, E, F, G, H) with the FDs: A \rightarrow C, BC \rightarrow AD, C \rightarrow BF, D \rightarrow H, and F \rightarrow AE, is \{A, G\} a key of R? Prove your answer and describe your proof strategy including all the steps you utilize in the proof.