Subjects set theory

Disjoint Sets

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Disjoint Sets


1. **Problem Statement:** Represent the information that sets P and Q are two disjoint sets in a universal set using a Venn diagram. 2. **Understanding the Problem:** Two sets are disjoint if they have no elements in common, i.e., their intersection is empty: $$P \cap Q = \emptyset$$. 3. **Formula and Rules:** - Universal set: $$U$$ contains all elements under consideration. - Disjoint sets: $$P \cap Q = \emptyset$$ means no overlap. 4. **Representation:** - Draw a rectangle to represent the universal set $$U$$. - Inside the rectangle, draw two circles labeled $$P$$ and $$Q$$ that do not overlap. 5. **Explanation:** Since $$P$$ and $$Q$$ are disjoint, their circles do not intersect. All elements of $$P$$ and $$Q$$ lie inside $$U$$ but separately. Final answer: The Venn diagram shows two non-overlapping circles inside a rectangle representing $$U$$.