The expression \(\emptyset \subseteq \emptyset\) (read as "the empty set is a subset of the empty set") is **true**. 

Here's why:

- The empty set \(\emptyset\) is a set that contains no elements.
- A set \(A\) is considered a subset of another set \(B\) (written \(A \subseteq B\)) if every element of \(A\) is also an element of \(B\).
- Since \(\emptyset\) has no elements, the condition "every element of \(\emptyset\) is also an element of \(\emptyset\)" is vacuously true. Therefore, \(\emptyset\) is a subset of itself.

Thus, \(\emptyset \subseteq \emptyset\) is indeed true.

Would you like more details or have any questions?

Here are five related questions you might consider:

1. What is the difference between \(\subset\) and \(\subseteq\)?
2. Can a set be a subset of itself if it is not empty?
3. What is the power set of the empty set?
4. How do you prove that any set is a subset of itself?
5. What does it mean for one set to be a proper subset of another?

**Tip:** When working with set theory, always remember that an empty set is a subset of every set, including itself.

Explore the concept of set theory with an explanation of the statement ∅ ⊆ ∅. Learn why the empty set is a subset of itself, supported by logical reasoning. This problem delves into fundamental set theory principles, suitable for advanced learners and enthusiasts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation