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 :) 

"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.
