Defining predicates in prolog

Question

Using prolog,

1. Define the predicate, conc(L1,L2,L3), where L3 is a concatenation of the two lists L1 and L2
2. Using above predicate, define the predicate One_after_first(X,L) is true iff item X occurs immediately after the first element in list L.

Answer 1

conc(L1, L2, L3) :- append(L1, L2, L3).

one_after_first(L, Y) :- conc([_ | [Y | []]], _, L).

This solution uses conc , but there is an easier solution:

one_after_first([_ | [Y | _]], Y).

You can call it with:

one_after_first([1,2,3,4], 2).