## anonymous 3 years ago Is this true or false? \[\emptyset \subset \emptyset \]

1. anonymous

I know that the empty set is a subset of every set but I'm not sure if its a subset of itself.

2. anonymous

It is a subset of itself because a subset of finite set also contains that set.

3. anonymous

It depends if you mean just subset and proper subset. One allows the set to be a subset of itself, and the other doesn't.

4. anonymous

This is really a matter of semantics, since there are notational inconsistencies regarding \( \subset\) and \( \subseteq \)

5. anonymous

I mean proper subset. I think its false.

6. anonymous

but considering just a subset is TRUE.

7. anonymous

It is false for a proper subset, but it is a subset.

8. anonymous

ya its not a proper subset of itself, but it sure is a subset of itself

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