Decide whether the symbol 

is a proper subset of⊂​, 

is a subset of⊆​, both, or neither can be placed in the blank to make the statement true.


To decide whether the symbol that makes the statement true is "⊂" (proper subset), "⊆" (subset), both, or neither, we need the sets involved. Let's review the definitions of these subset relations:

- **Subset (⊆)**: Set \( A \) is a subset of set \( B \) (denoted \( A \subseteq B \)) if every element of \( A \) is also an element of \( B \). This includes the possibility that \( A = B \) (i.e., they can be the same set).
  
- **Proper Subset (⊂)**: Set \( A \) is a proper subset of set \( B \) (denoted \( A \subset B \)) if every element of \( A \) is also an element of \( B \), but \( A \neq B \). That is, \( A \) must be strictly smaller than \( B \).

Without the specific sets involved, I cannot definitively state which symbol applies to your problem, but I can tell you how to decide:

- If the sets are identical, only "⊆" is correct because a proper subset requires that the sets be different.
- If one set is strictly smaller than the other, both "⊂" and "⊆" would be true.

Would you like to share the specific sets or give more details for clarification?

### Related Questions:
1. What is the difference between a subset and a proper subset?
2. Can a set be a proper subset of itself?
3. How can you determine if one set is a subset of another?
4. What are some examples where "⊆" holds but "⊂" does not?
5. How does the empty set relate to subsets and proper subsets?

### Tip:
A set is always a subset of itself but never a proper subset of itself.

Decide whether the symbol is a proper subset of ⊂, is a subset of ⊆, both, or neither can be placed in the blank to make the statement true.

Learn how to determine if a set is a subset (⊆) or a proper subset (⊂) in set theory. Understand the difference between these two concepts with clear definitions and examples. Suitable for high school students in Grades 9-12.

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