Definitions:
1. If every member of set A is also a member of set B, then A is a subset of B, we write A ⊆ B. We can say A is contained in B.
In your example: {} ⊆ {0}, {} ⊆ {1}.
2. We can also say B ⊇ A, B is a superset of A, B includes A, or B contains A.
In your example: {0} ⊇ {}, {1} ⊇ {}.
3. If A is not a subset of B, we write A ⊈ B.
In your example: {0} ⊈ {1}
Note that:
The empty set denoted by ∅ or {} is a subset of any set.
