Is the empty set a superset of itself?

Question

I know the empty set is a subset of itself, so I'm assuming that it's also the case that it is a superset of itself?

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Does this answer your question? Is the empty set a subset of itself? — Greg Nisbet, Jan 02 '21 at 19:46
Yes. $A \subseteq B \iff B\supseteq A$ so .... $\emptyset \subseteq \emptyset \iff \emptyset\supseteq \emptyset$..... Furthermore 1: Everyset is a subset and a superset of itself 2: The empty set is a subset of every set. And 2: every set is a superset of the emptyset. — fleablood, Jan 02 '21 at 19:53

score 4 · Accepted Answer · answered Jan 02 '21 at 19:23

4

Yes. In the same way that every set is a superset of itself, but not a proper superset.

answered Jan 02 '21 at 19:23

Asaf Karagila

And the same way that every set is a superset of the empty set. – Andreas Blass Jan 02 '21 at 19:53

score 2 · Answer 2 · answered Jan 02 '21 at 19:56

Yes. $A \subseteq B \iff B\supseteq A$ so .... $\emptyset \subseteq \emptyset \iff \emptyset\supseteq \emptyset$

..... Furthermore

Every set is a subset and a superset of itself. Or in other words $A \subseteq A$ and $A\supseteq A$ for all sets $A$. (This holds true even if $A$ is the empty set.)
The empty set is a subset of every set. Or in other words $\emptyset \subseteq A$ for all sets $A$. (This holds true even if $A$ is the empty set.) And
Every set is a superset of the empty set. or in other words $A \supseteq \emptyset$ for all sets $A$. (This holds true ev.... well, you know the drill.)

2 Answers2