1. The problem involves understanding and verifying set operations given the sets A and B. 2. The union of sets A and B, denoted $A \cup B$, includes all elements that are in A, or B, or both. Here, $A \cup B = \{a, b, c, d, e\}$. 3. The intersection of sets A and B, denoted $A \cap B$, includes only elements common to both sets. Here, $A \cap B = \{c\}$. 4. The complement of set A, denoted $A'$, includes all elements not in A but in the universal set. Here, $A' = \{d, e, f, g\}$. 5. The difference of sets A and B, denoted $A \sim B$, includes elements in A but not in B. Here, $A \sim B = \{a, b\}$. 6. The symmetric difference of sets A and B, denoted $A \oplus B$, includes elements in either A or B but not in both. Here, $A \oplus B = \{a, b, d, e\}$. These operations follow standard set theory rules and the elements listed match the definitions of each operation.