3. Let \( A=\{1,2,3,4,5\}, B=\{2,4,6\}, C=\{3,4,5\} \) and let \( E=\{0,1,2,3,4,5,6,7,8\} \) Find \( \begin{array}{lllll}\text { i) } B^{\prime} & \text { ii) } A \cup B & \text { iii) } A \cap B & \text { iv) }(A \cup B)^{\prime} & \text { v) }(A \cap B)^{\prime}\end{array} \) vi) \( C-B \)

Alright, let’s dive into the magical world of sets and perform some operations! i) \( B' = E - B = \{0, 1, 3, 5, 7, 8\} \) This represents all the elements in \( E \) that are not in \( B \). ii) \( A \cup B = \{1, 2, 3, 4, 5\} \cup \{2, 4, 6\} = \{1, 2, 3, 4, 5, 6\} \) This is the union, which combines all unique elements from both sets. iii) \( A \cap B = \{1, 2, 3, 4, 5\} \cap \{2, 4, 6\} = \{2, 4\} \) The intersection gives us the elements common to both sets. iv) \( (A \cup B)' = E - (A \cup B) = E - \{1, 2, 3, 4, 5, 6\} = \{0, 7, 8\} \) This shows us what’s outside the union of \( A \) and \( B \) within the universal set \( E \). v) \( (A \cap B)' = E - (A \cap B) = E - \{2, 4\} = \{0, 1, 3, 5, 6, 7, 8\} \) Here, we identify what’s outside the intersection of \( A \) and \( B \). vi) \( C - B = C \setminus B = \{3, 4, 5\} - \{2, 4, 6\} = \{3, 5\} \) This gives us the elements in \( C \) that are not present in \( B \). And there you have it, a complete breakdown of set operations with a sprinkle of set magic!