Consider a relation R with attributes ABCDEFGH and functional dependencies S: S $=\{$A$->$CD$,$ ACF$->$G$,$ AD$->$BEF, BCG$->$D$,$ CF$->$AH$,$ CH$->$G$,$ D$->$B$,$ H$->$DEG$\}1.$ Compute all keys for R$.2.$ Compute a minimal basis for S$.$ In your final answer, put the FDs into alphabetical order. $3.$ Using the minimal basis from the previous step, employ the $3$NF synthesis algorithm to obtain a lossless and dependencypreserving decomposition of relation R into a collection of relations that are in $3$NF$.4.$ Does your schema allow redundancy? Explain all your answers and show your rough work.