These statements are based on the fundamental laws of operations on sets, specifically the complement laws. In the context of the provided exercise questions which utilize the universal set $U$ and empty set $\phi$:

(i) $A \cup A' = U$: The union of a set and its complement includes all elements in the universal set. (ii) $\phi' \cap A = A$: The complement of the empty set is the universal set ($\phi' = U$). The intersection of the universal set with any set $A$ is the set $A$ itself. (iii) $A \cap A' = \phi$: A set and its complement are disjoint sets; their intersection is the empty set. (iv) $U' \cap A = \phi$: The complement of the universal set is the empty set ($U' = \phi$). The intersection of the empty set with any set $A$ is the empty set.