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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 Vega Davison. in South Africa
Mar 15,2025

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**Question 3** **(a)** Given: \[ E = \{\text{cat, dog, rabbit, mouse}\},\quad F = \{\text{dog, cow, duck, pig, rabbit}\},\quad G = \{\text{mouse, python}\} \] 1. \((E \cap F) \cup G = \{\text{dog, rabbit, mouse, python}\}\) 2. \(E \cap (F \cup G) = \{\text{dog, rabbit, mouse}\}\) 3. \((E \cap F)' \cap G = \{\text{mouse, python}\}\) **(b)** Given: \[ \mathbf{U} = \{2,3,4,5,6,7,8,9,10,11\},\quad A = \{3,5,7,9,11\},\quad B = \{7,8,9,10,11\} \] 1. \((\mathbf{U} \cap A) \cup (\mathbf{U} \cap B) = \{3,5,7,8,9,10,11\}\) 2. \((A - B)' = \{2,4,6,7,8,9,10,11\}\) --- **Question 4** In a Venn diagram: 1. \(A \cup B\) includes all elements in \(A\) or \(B\) (or both). 2. \(A \cap B\) includes elements common to both \(A\) and \(B\). 3. \(A \cap B\) (same as above). 4. \(B \cap A\) (same as \(A \cap B\)). 5. \((A \cup B)'\) includes elements not in \(A\) or \(B\).

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Beyond the Answer

When we dive into sets and Venn diagrams, we're exploring the essence of relationships in mathematics! Sets are magical little collections that help us organize and understand data. For example, did you know that Venn diagrams were introduced by John Venn in 1880? They’re not just tools for math classes; they’re often used in logic, statistics, and even computer science! Now, as you tackle these problems, remember common pitfalls: when computing intersections and unions, it's easy to forget to meticulously list all elements without duplication. Always pay attention to the universal set context, especially when dealing with complements! To avoid confusion, draw your diagrams neatly, label them well, and keep track of your elements. Happy calculating!

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