I think these examples should straighten things out. Have your definitions handy:
A set S is a subset of set T iff every member of S is also a member of T.
A set S is a proper subset of T iff S is a subset of T and there is some (at least one) member of T that isn't a member of S.
T = {{{}}}. Which of the following are subsets of T? Proper subsets?
A. {{{}}}
B. {{}}
C. {}
T = {{}, {{{}}}}. Which of the following are subsets of T? Proper subsets?
A. {{}, {{{}}}}
B. {{{{}}}}
C. {{{}}}
D. {{}}
E. {}
