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 \( F=\{2,3,4\} \).
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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!