Write Prolog procedures that can be used to perform the following operations on lists:

NB: use Prolog built$-$in predicates for Questions $3\mathrm{.}13\mathrm{.}3$:

$1.$ Write a Prolog procedure add$\_$element$($X$,$L$,$L$1)$ that adds element X to list L$.$

$2.$ Lists can be used to represent sets in Prolog. Write a Prolog procedure sym$\_$diff$($A$,$B$,$L$)$ that returns the symmetric difference between sets A and B giving L$.$ The set L contains all elements that either belong to A or to B but not to both.

$3.$ Define a predicate occurrences$($X$,$L$,$N$)$ that holds iff the element X occurs N times in the list L$.$