a$.$ Consider the relation R$($L$,$M$,$N$,$O$,$P$,$Q$)$ and a set of functional dependencies

F $=\{$LNO$->$M$,$ MN$->$LOP, N$->$O$,$ OP$->$LN$\}.$

$[2$pt$]$ Can we infer NP $->$ LM from F $?$ Show your work

$[3$pt$]$ Can we infer NQ $->$ LO from F $?$ Show your work

b$.[10$ pt$]$ Consider R $($O$,$P$,$Q$,$R$,$S$,$T$)$ to be a relation schema, and let

F $=\{$O $->$ P$,$ Q $->$ O$,$ PR $->$ Q$,$ RS $->$ T$\}$ be a set of func$$onal dependencies $($FDs$).$

$$ Infer at least five new FDs by using Armstrong$$s axioms and their derived

inference rules. You must use a different rule per answer