Compare the possible meanings
| Notation | Typical meaning | How to identify it |
|---|---|---|
A ⊆ B | Subset, equality allowed | Unambiguous |
A ⊂ B | Subset or proper subset | Convention varies |
A ⊊ B | Proper subset | Equality excluded explicitly |
A ⊈ B | Not a subset | Counterexample element exists |
Examples
- {1,2}⊆{1,2} is true.
- {1}⊊{1,2} is true.
- A text using ⊂ should define whether equality is allowed.
How to decide
Prefer ⊆ for subset-with-possible-equality and ⊊ for proper subset when writing for mixed audiences.
How to verify the interpretation
Test both containment and equality, then compare with the document's notation convention.