Consider the sets X and Y. Write the statement in symbols.
A union of complements

The statement "A union of complements" can be written in set notation as follows:

\[
X^c \cup Y^c
\]

This represents the union of the complements of sets \( X \) and \( Y \). Here, \( X^c \) and \( Y^c \) are the complements of sets \( X \) and \( Y \), respectively, and the symbol \( \cup \) denotes the union.

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Here are 5 related questions:
1. How would you express the intersection of complements symbolically?
2. What is the complement of the union of \( X \) and \( Y \)?
3. How does De Morgan's Law relate to unions and complements?
4. Can you describe the relationship between \( X \cup Y \) and \( X^c \cup Y^c \)?
5. What does it mean if the complement of \( X \cup Y \) equals the complement of \( X \)?

**Tip:** De Morgan's Laws are essential when working with unions and intersections of complements. They help simplify expressions involving complements.

Consider the sets X and Y. Write the statement in symbols. A union of complements.

Explore the union of complements in set theory, symbolized as X^c ∪ Y^c. This problem delves into key set theory concepts such as unions, complements, and their relation to De Morgan's Laws. Suitable for high school students in Grades 9-12.

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