$1.$Provide a justification or a short proof for the following statements after you determined they are TRUE or FALSE. $(8$ marks: $2$ marks for each$)$a$)$ F$($n$)=\backslash$Omega $($g$($n$))$ is like saying f$($n$)>=$ g$($n$).$b$)$ A maximum weight edge of a connected, undirected graph with distinct edge weights is neverincluded in a minimum spanning tree.c$)$ NP$-$hard $$ NP$.$d$)$ IfSubset$-$Sum$$PthenSAT$$P$.$e$)$ if problem a can be reduced to $3$SAT via a deterministic polynomial time reduction yhen A belongs to NPthen A is NP complete true or false