Final answer:
The question involves set theory, specifically the properties that define a partition of the real numbers into two subsets, L and U, which do not overlap and together comprise all real numbers.
Step-by-step explanation:
The question pertains to the mathematical concept of set theory. It describes two sets, L and U, that have specific relationships with each other and with the real number set R. The question states that set L and set U are subsets of the real numbers (R), such that L intersect U (L∩U) is the empty set (meaning they have no elements in common), the union of L and U (L∪U) is equal to the entire set of real numbers (R), and neither L nor U are empty sets (each contains at least one element). This describes a partition of R into two non-empty, non-overlapping subsets.