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Question 3 a) Suppose \( E=\{ \) cat, dog, rabbit, mouse \( \}, F=\{ \) dog, cow, duck, pig, rabbit \( \} \) mouse, python \( \} \) Find the following: 1. \( (E \cap F) \cup G \) 2. \( E \cap(F \cup G) \) 3. \( (E \cap F)^{\prime} \cap G \) b) If \( \mathbf{U}=\{2,3,4,5,6,7,8,9,10,11\}, A=\{3,5,7,9,11\} \) and \( B=\{7,8,9,10,11\} \) 1. Then find \( (\mathbf{U} \cap A) \cup(\mathbf{U} \cap B) \), 2. and also find \( (A-B)^{\prime} \). Question 4 By the use of a venn diagram, answer the following questions: 1. \( A \cup B \) 2. \( A \cap B \) 3. \( A \cap B \) 4. \( B \cap A \) 5. \( (A \cup B)^{\prime} \)

Ask by Bowers Ortega. in South Africa
Mar 15,2025

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**3(a)** 1. \( (E \cap F) \cup G = \{\text{dog}, \text{rabbit}, \text{mouse}, \text{python}\} \) 2. \( E \cap (F \cup G) = \{\text{dog}, \text{rabbit}, \text{mouse}\} \) 3. \( (E \cap F)' \cap G = \{\text{mouse}, \text{python}\} \) **3(b)** 1. \( (\mathbf{U} \cap A) \cup (\mathbf{U} \cap B) = \{3,5,7,8,9,10,11\} \) 2. \( (A - B)' = \{2,4,6,7,8,9,10,11\} \) **4** 1. \( A \cup B \): All elements in \( A \) or \( B \) (or both). 2. \( A \cap B \): Elements common to both \( A \) and \( B \). 3. \( A \cap B \): Same as item 2. 4. \( B \cap A \): Same as \( A \cap B \). 5. \( (A \cup B)' \): Elements not in \( A \) or \( B \).

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Bonus Knowledge

To truly understand the beauty of set operations, let’s journey back to the realms of ancient mathematicians. The concept of sets dates back to Georg Cantor in the late 19th century. He revolutionized mathematics with his theories, elevating the topic to new heights! His work paved the way for modern set theory, whose applications touch everything from computer science to statistics. Now, when it comes to applying set operations in the real world, think of social media. Each user can be seen as a set of interests - overlapping hobbies create intersections (like your friends who love both hiking and biking), while the total collection of users might represent the union. By mastering set operations, you’ll be able to categorize and analyze information much like a pro, optimizing connections!

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