Math Problem Statement
∅⊆∅
Solution
The expression (read as "the empty set is a subset of the empty set") is true.
Here's why:
- The empty set is a set that contains no elements.
- A set is considered a subset of another set (written ) if every element of is also an element of .
- Since has no elements, the condition "every element of is also an element of " is vacuously true. Therefore, is a subset of itself.
Thus, is indeed true.
Would you like more details or have any questions?
Here are five related questions you might consider:
- What is the difference between and ?
- Can a set be a subset of itself if it is not empty?
- What is the power set of the empty set?
- How do you prove that any set is a subset of itself?
- 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.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Formulas
-
Theorems
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Suitable Grade Level
Advanced
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