**Theorem Statement:**Prove that for all sets \( A \) and \( B_1, B_2, \ldots, B_n \),\[A - \bigcap_{i=1}^{n} B_i = \bigcup_{i=1}^{n} (A - B_i).\]**Explanation:**This theorem involves set operations, specifically focusing on the relationships between set differences, intersections, and unions.1. **Set Difference** \((A - B)\): This denotes the set of elements that are in \( A \) but not in \( B \).2. **Intersection** \(\bigcap_{i=1}^{n} B_i\): This represents the set of elements common to all sets \( B_1, B_2, \ldots, B_n \).3. **Union** \(\bigcup_{i=1}^{n} (A - B_i)\): This is the set of elements that are in either \( A - B_1, A - B_2, \ldots, \) or \( A - B_n \).The theorem states that the set difference between \( A \) and the intersection of \( B_1, B_2, \ldots, B_n \) is equivalent to the union of the set differences of \( A \) with each \( B_i \).

Name: **Theorem Statement:**Prove that for all sets \( A \) and \( B_1, B_2
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: **Theorem Statement:**Prove that for all sets \( A \) and \( B_1, B_2, \ldots, B_n \),\[A - \bigcap_{i=1}^{n} B_i = \bigcup_{i=1}^{n} (A - B_i).\]**Explanation:**This theorem involves set operations, specifically focusing on the relationships betwee