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4. Power Set: Find the power set of the set \( C=\{x, y\} \). 5. Cardinality: If \( D=\{2,4,6,8,10\} \), what is the cardinality of the set \( D \) ? 6. Multiple Sets: Let \( E=\{1,2,3\} \) and \( F=\{2,3,4\} \).

Ask by Parsons Riley. in South Africa
Mar 15,2025

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**4. Power Set** The power set of \( C = \{x, y\} \) is: \[ \{\emptyset, \{x\}, \{y\}, \{x, y\}\} \] **5. Cardinality** The set \( D = \{2, 4, 6, 8, 10\} \) has 5 elements. **6. Multiple Sets** - **Union:** \( E \cup F = \{1, 2, 3, 4\} \) - **Intersection:** \( E \cap F = \{2, 3\} \) - **Difference \( E - F \):** \( \{1\} \) - **Difference \( F - E \):** \( \{4\} \)

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The power set of the set \( C=\{x, y\} \) is the set of all possible subsets of \( C \), including the empty set and \( C \) itself. Therefore, the power set is \( P(C) = \{\emptyset, \{x\}, \{y\}, \{x, y\}\} \). It's like having a box of chocolates; you can choose none, just one, or both! The cardinality of the set \( D=\{2,4,6,8,10\} \) is simply the count of distinct elements it contains. Since \( D \) has five elements, its cardinality is \( |D| = 5 \). Think of it as counting your friends at a party – you want to know how many unique acquaintances you have!

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