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Is this true or false? \[\emptyset \subset \emptyset \]
I know that the empty set is a subset of every set but I'm not sure if its a subset of itself.
It is a subset of itself because a subset of finite set also contains that set.
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.
This is really a matter of semantics, since there are notational inconsistencies regarding \( \subset\) and \( \subseteq \)
I mean proper subset. I think its false.
but considering just a subset is TRUE.
It is false for a proper subset, but it is a subset.
ya its not a proper subset of itself, but it sure is a subset of itself