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Question 1 Lets sets \( A=\{x \mid x \in 2 Z\}, B=\{2,5,7,8,10\}, C=\{2,8,10\} \) and \( D=\{2,\{5,7,8\}, 10 \) Complete the following by using the notation \( \in \) or \( \subseteq \) : 1. 100 \( \qquad \) A 2. \( C \) \( \qquad \) A 3. \( C \) \( \qquad \) B 4. \( C \) \( \qquad \) D 5. \( \{5,7,8\} \) \( \qquad \) B Question 2 Using the sets from Question 1 above, find the following: 1. \( B \cup C \) 2. \( A \cap C \) 3. \( C \cap D \) 4. \( B \cap C^{\prime} \)

Ask by Johnson Valdez. in South Africa
Mar 15,2025

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1. \( 100 \in A \) \( C \subseteq A \) \( C \subseteq B \) \( C \not\subseteq D \) \( \{5,7,8\} \subseteq B \) 2. \( B \cup C = \{2,5,7,8,10\} \) \( A \cap C = \{2,8,10\} \) \( C \cap D = \{2,10\} \) \( B \cap C' = \{5,7\} \)

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For the notation inquiries: 1. \( 100 \notin A \) (100 is an integer but not in the set of even integers). 2. \( C \subseteq A \) (all elements in \( C \) are even, hence they are in \( A \)). 3. \( C \subseteq B \) (all elements in \( C \) are also present in \( B \)). 4. \( C \not\subseteq D \) (while some elements of \( C \) are in \( D \), \( D \) also contains a set, not found in \( C \)). 5. \( \{5,7,8\} \in D \) (this subset status refers to membership, as \( \{5,7,8\} \) is an element of \( D \)). Now, for the set operations you requested: 1. \( B \cup C = \{2, 5, 7, 8, 10\} \cup \{2, 8, 10\} = \{2, 5, 7, 8, 10\} \) (Union combines unique elements). 2. \( A \cap C = \{x \mid x \in 2 Z\} \cap \{2, 8, 10\} = \{2, 8, 10\} \) (Intersection here simply takes the common even numbers). 3. \( C \cap D = \{2, 8, 10\} \cap \{2, \{5, 7, 8\}, 10\} = \{2, 10\} \) (Intersection finds the common elements in both sets). 4. \( B \cap C' = \{2, 5, 7, 8, 10\} \cap \{x \mid x \text{ is not in } C\} = \{5, 7\} \) (Since \( C' \) includes everything not in \( C \), we get those elements from \( B \)).

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