# is an empty set an element of {empty set}

I am on set section right now and I have questions about empty set

is an empty set an element of {empty set}? is an empty set a subset of {empty set}? is an empty set a proper subset of {empty set}?

I am just wondering because on the textbook didn't mention about these three? please bear with me I am really doubt a lot of things.

I got the questions online and I am practicing it right now so please

correct me if I am wrong. a) {empty set} is an element of {empty set} = false b) {empty set} is a subset of {empty set} = false c) empty set is an element of {empty set,{empty set}}= true d) {empty set} is an element of {{empty set}} = true e) {{empty set}}is a proper subset of {empty set,{empty set}} = false

I hope I get em all right after you explained to me.

thank you :)

## 2 Answers

"is an empty set an element of {empty set}?"

Yes, the set {empty set} is a set with a single element. The single element is the empty set. {empty set} is NOT the same thing as the empty set.

" is an empty set a subset of..." STOP!!! The empty set is a subset of EVERY set. (Because the empty set has no elements so all zero of its elements are in every other set. Or if you take A and B, A $\subset$ B means A doesn't have any elements not in B. The element doesn't have any elements not in B so empty set $\subset B and it doesn't matter what B is. "is an empty set a proper subset of ..." Yes. A proper subset is a subset that isn't the same set. empty set is not {empty set} so it is a proper subset. • then is {empty set} an element of {empty set} ? it is not right? – guest1 Oct 14 '15 at 5:52 • @guest1,$\{\emptyset\}\not\in\{\emptyset\}$because the only element of$\{\emptyset\}$is$\emptyset$and$\emptyset\ne\{\emptyset\}\$. – Martín-Blas Pérez Pinilla Oct 15 '15 at 6:53
• The thing we are getting at is having a set as a member of another set, is not at all the same thing as have the elements of the set be a member of the other set. The {{banana, orange}, fred the dinosaur, 7} has exactly 3 members; the number 7, fred the dinosaur, and the set {banana, orange}. It does not actually have either banana or orange as a member. It has a set that contains banana and orage but it is the set that is the member. Not banana or orange. Same thing as {empty set} which is a set with exactly one member. – fleablood Oct 15 '15 at 7:10

A empty set {} has no entries... It is subset of every other set but a set containing the empty set is not empty anymore ... (It contains the empty set)