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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**4. Power Set**

The power set $$ \mathcal{P}(C) $$ of a set $$ C $$ is the set of all subsets of $$ C $$. For $$ C = \{x, y\} $$, its subsets are:  
$$
\emptyset,\ \{x\},\ \{y\},\ \{x, y\}
$$
Thus, the power set is:
$$
\mathcal{P}(C) = \{\emptyset, \{x\}, \{y\}, \{x, y\}\}
$$

**5. Cardinality**

The cardinality of a set is the number of elements it contains. For $$ D = \{2, 4, 6, 8, 10\} $$, there are 5 elements. Hence, the cardinality of $$ D $$ is:
$$
|D| = 5
$$

**6. Multiple Sets**

Given $$ E = \{1, 2, 3\} $$ and $$ F = \{2, 3, 4\} $$, we can consider several operations:

- **Union:**  
  The union $$ E \cup F $$ is the set of elements that are in $$ E $$, in $$ F $$, or in both:
  $$
  E \cup F = \{1, 2, 3, 4\}
  $$

- **Intersection:**  
  The intersection $$ E \cap F $$ is the set of elements that are common to both $$ E $$ and $$ F $$:
  $$
  E \cap F = \{2, 3\}
  $$

- **Difference:**  
  The difference $$ E - F $$ is the set of elements that are in $$ E $$ but not in $$ F $$:
  $$
  E - F = \{1\}
  $$
  Similarly, the difference $$ F - E $$ is:
  $$
  F - E = \{4\}
  $$
**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 $$ F - E $$:** $$ \{4\} $$

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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