Let U be the universal set, where: U= 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 Let sets A, B and C be subsets of U, where: A= 3,6,7,10,13,15 B= 3,6,8,9,15 C= 5,7,10,13,16,18,19 Find the following: LIST the elements in the set B'cup 0 B'cup O={ 1,2,4,5,7,1,1,1,1,2,13,14,16,17,1 Enter the elements as a list, separated by commas. If the result is the empty set , enter DNE LIST the elements in the set Bcap C Bcap C={ 3,6,10,13,15 Enter the elements as a list, separated by commas. If the result is the empty set enter DNE LIST the elements in the set B'cup C B'cup C={ 1,2,4,5,7,10,11,12,13,16,16,17,1 Enter the elements as a list, separated by commas. If the result is the empty set,enter DNE LIST the elements in the set (Bcap C)cap A' (Bcap C)cap A'=(10,13 Enter the elements as a list, separated by commas. If the result is the empty set enter DNE

Let's correct the calculations and ensure the results are accurate:<br /><br />1. **Finding \( B' \cup 0 \):**<br /><br /> First, find the complement of \( B \) with respect to \( U \):<br /> \[<br /> B' = U - B = \{1, 2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19\}<br /> \]<br /><br /> Now, union with 0:<br /> \[<br /> B' \cup 0 = \{0\} \cup \{1, 2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19\} = \{0, 1, 2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19\}<br /> \]<br /><br /> So, the elements in the set \( B' \cup 0 \) are:<br /> \[<br /> \{0, 1, 2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19\}<br /> \]<br /><br />2. **Finding \( B \cap C \):**<br /><br /> Intersection of sets \( B \) and \( C \):<br /> \[<br /> B \cap C = \{3, 6, 8, 9, 15\} \cap \{5, 7, 10, 13, 16, 18, 19\} = \{10, 13\}<br /> \]<br /><br /> So, the elements in the set \( B \cap C \) are:<br /> \[<br /> \{10, 13\}<br /> \]<br /><br />3. **Finding \( B' \cup C \):**<br /><br /> First, find the complement of \( B \) with respect to \( U \):<br /> \[<br /> B' = U - B = \{1, 2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19\}<br /> \]<br /><br /> Now, union with \( C \):<br /> \[<br /> B' \cup C = \{1, 2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19\} \cup \{5, 7, 10, 13, 16, 18, 19\} = \{1, 2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19\}<br /> \]<br /><br /> So, the elements in the set \( B' \cup C \) are:<br /> \[<br /> \{1, 2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19\}<br /> \]<br /><br />4. **Finding \( (B \cap C) \cap A' \):**<br /><br /> First, find the complement of \( A \) with respect to \( U \):<br /> \[<br /> A' = U - A = \{1, 2, 4, 5, 8, 9, 11, 12, 14, 16, 17, 18, 19\}<br /> \]<br /><br /> Now, intersection with \( B \cap C \):<br /> \[<br /> (B \cap C) \cap A' = \{10, 13\} \cap \{1, 2, 4, 5, 8, 9, 11, 12, 14, 16, 17, 18, 19\} = \{13\}<br /> \]<br /><br /> So, the elements in the set \( (B \cap C) \cap A' \) are:<br /> \[<br /> \{13\}<br /> \]<br /><br />To summarize:<br /><br />1. \( B' \cup 0 = \{0, 1, 2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19\} \)<br />2. \( B \cap C = \{10, 13\} \)<br />3. \( B' \cup C = \{1, 2, 4, 5