Consider the relation R$($W$,$ X$,$ Y$,$ Z$)$ with a set of functional dependencies F given by:

$1.$WY $->$X

$2.$X $->$Z

$3.$ Z $->$Y

$4.$W $->$Y

$1-$Find the minimal cover of F$.$

$2-$Calculate the closure of $\{$W$\}.$

$3-$Determine the candidate keys of R$.$

$4-$Analyze the normal forms. Based on your candidate keys and the minimal cover, determine the highest normal form $(1$NF$,2$NF$,3$NF$,$ BCNF$)$ satisfied by the relation R$.$