Let us recall the definition for the set of linked lists L defined in class: Basis Step: I EL Recursive Step: If I EL, and n e N, then (n,1) EL We now define 3 functions on this linked list as: i) nodes : L + P(N) Basis Step: nodes([]) = 0 Recursive Step: If IEL, ne N, then nodes((n,1)) = {n} U nodes(1) ii) sum: LN Basis Step: sum([]) = 0 Recursive Step: If I EL, EN, then sumi(n,1)) = n + sum(1) iii) length: LN Basis Step: length([]) = 0 Recursive Step: If IEL, n E N, then length((n,1)) = 1 + length(1) a) Consider the proposition given as: VIEL, SCEN, Vx N(x