Problem$4.(25$points$)$

Given the relation below and the associated functional dependencies:

$A=(M,N,P,Q,R,S,T,U,V,W,x)$

xUV$Q$

$RM$

$NU$

$WP$

$STV$

$xW$

$SNx$

$UR$

$($a$)$ List the primary key for this relation. Explain your answer. Clearly state the PK $(5$ points$)$

$($b$)$ Assuming the table is in First Normal Form, put the table in Second Normal Form. Explain your answer and clearly designate your primary keys for each table. $(5$ points$).$

$($c$)$ Put the table in third normal form. Explain your answer and clearly designate your primary keys. You must show all the tables. $(5$ points$)$