Intersection
it seems a little like cheating to me to use a HashSet here. I would probably write my own contains method for the linked list (which is bad for performance, but performance is not really the point here).
Other than that:
largerListNode != null
This check seems unnecessary. It's the larger list, after all. items.size() > 0 should always catch this.
Union
The return value should probably not be named intersectionlist :) It also does not do union. The code should look something like this:
public IntersectionAndUnionLinkedList<T> union(IntersectionAndUnionLinkedList<T> list) {
// ... in case this list should not be changed, copy it first. Otherwise, this list will be result of the union
// traverse through the input list. add nodes from input list to beginning of this list
Node listCurrentNode = list.first;
while (listCurrentNode != null) {
// ... if you do not want duplicate elements, check for them. or remove them at the end
Node listNextNode = listCurrentNode.next;
Node thisPreviousFirstNode = this.first;
listCurrentNode.next = thisPreviousFirstNode;
this.first = listCurrentNode;
listCurrentNode = listNextNode;
}
return this;
}
Another (slower) approach would be to create a new list (the output list), and traverse both input lists one at a time, adding their elements to the new list (if it does not already contain the item).
General
The diamond operator is only supported since Java 7. So I would still use this:
Node<T> node = new Node<T>(item);
instead of this
Node<T> node = new Node<>(item);
if possible.
