Final answer:
Elizabeth and Edgar, being the children of brothers Fred and Frank, respectively, are first cousins. They share a set of grandparents.
Step-by-step explanation:
If Fred and Frank are brothers and they each have a child, with Fred's child being Elizabeth and Frank's child being Edgar, then Elizabeth and Edgar would be first cousins to each other. First cousins share a set of grandparents; in this case, the parents of Fred and Frank are the shared grandparents of Elizabeth and Edgar. This connection is a result of family ties and lineage, often important in understanding family relationships and genealogy.